Channel coding method and apparatus in communication system

ABSTRACT

Embodiments of this application provide a method for transmitting encoded information. A communication device obtains K bits of information, and generates a to-be-encoded sequence u1N, wherein N is a length of the sequence. The device encodes the sequence u1N in an encoding process, to obtain an output sequence, and transmits the output sequence. In the sequence u1N, each of the N bits corresponds to a subchannel, and each subchannel has a reliability. The K information bits, a quantity J of first-type auxiliary bits, and a quantity J′ of second-type auxiliary bits are placed in K′=K+J+J′ bit positions of the sequence u1N according to reliabilities of the subchannels. Since the positions of the information bits and the auxiliary bits are pre-determined and not affected by subsequent encoding and rate-matching, overheads of real-time reliability calculation are effectively reduced, time is saved, and delay is reduced.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/CN2018/080392, filed on Mar. 24, 2018, which claims priority toChinese Patent Application No. 201710184933.4, filed on Mar. 24, 2017.The disclosures of the aforementioned patent applications are herebyincorporated by reference in their entireties.

TECHNICAL FIELD

This application relates to communications technologies, and inparticular, to a polar code encoding method and apparatus, and a polarcode decoding method and apparatus.

BACKGROUND

Polar code is a new type of channel encoding scheme proposed byProfessor E. Ankan in 2008. The polar code is designed based on channelpolarization, and is the first constructive encoding scheme that can beproven, through a strict mathematical method, to achieve a channelcapacity. The polar code is a type of linear block code. A generatormatrix of the polar code is G_(N), and an encoding process of the polarcode isx ₁ ^(N) =u ₁ ^(N) G _(N),where u₁ ^(N)=(u₁, u₂, . . . u_(N)) is an N-bit binary row vector(namely, a code length of u₁ ^(N) is N), x₁ ^(N) is an N-bit encoded rowvector, G_(N) is an N×N matrix, and G_(N)=F₂ ^(⊗(log) ² ^((N))). Herein,

${F_{2} = \begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}},$and F₂ ^(⊗(log) ² ^((N))) is defined as a Kronecker product of aquantity log₂ N of matrices F₂. For example,

$F = \begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}$ $F^{\otimes 2} = \begin{bmatrix}1 & 0 & 0 & 0 \\1 & 1 & 0 & 0 \\1 & 0 & 1 & 0 \\1 & 1 & 1 & 1\end{bmatrix}$ $F^{\otimes 3} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\end{bmatrix}$

In the polar code encoding process, some bits in u₁ ^(N) are used tocarry information, and are referred to as information bits. Each bit inu₁ ^(N) has an index, and an index set of the information bits is markedas A. The other bits are set to a fixed value (referred to as fixedbits) pre-agreed on by a receive end (receiving device) and a transmitend (transmitting device), and an index set of these bits is representedby a complementary set A^(c) of A. Generally, these fixed bits areusually set to 0. Alternatively, a fixed bit sequence may be randomlyset as pre-agreed on by the receive end and the transmit end. Therefore,an encoding output of the polar code may be simplified as x₁^(N)=u_(A)G_(N)(A). Herein, u_(A) is an information bit set in u₁ ^(N),and u_(A) is a row vector of a length K, in other words, |A|=K, where|A| represents a quantity of elements in the set A, and K is aninformation block size. G_(N)(A) is a submatrix obtained from rows inthe matrix G_(N) that are corresponding to indexes in the set A, andG_(N)(A) is a K row×N column matrix. A polar code construction processis a process of selecting the set A, and the selection of set Adetermines polar code performance.

To improve the polar code performance, check precoding is usuallyperformed on information bits before performing the polar encoding. Thisis called check precoding cascaded polar encoding. There are two commoncheck precoding manners: cyclic redundancy check (CRC) cascaded polarencoding and parity check (PC) cascaded polar encoding. It may beconsidered that both CRC bits and PC bits are auxiliary bits. Generally,a CRC bit is usually considered as a special information bit, and isplaced on a subchannel (bit position) that is more reliable than theinformation bit, but PC bit position selection has not yet been defined.In the prior art, an auxiliary bit position is usually determined basedon reliability or a row weight of each subchannel that is calculated inreal time, and this is time-consuming and is not conducive to rapidimplementation. The embodiments of the present application provide asolution for rapidly determining an auxiliary bit position, so as toreduce encoding delay or decoding delay.

SUMMARY

This application provides a polar code encoding method and apparatus,and a polar code decoding method and apparatus, to rapidly determinepositions of second-type auxiliary bits including PC bits.

A first aspect of this application provides an encoding method. A mothercode length used in an encoding process is N, a code rate is R, a codelength obtained after encoding is M, a quantity of information bits isK, a quantity of first-type auxiliary bits is J, a quantity ofsecond-type auxiliary bits is J′, K+J+J′=K′, and the encoding methodincludes: selecting, by a sending device, K′ subchannels from Msubchannels to transmit the K information bits, the J first-typeauxiliary bits, and the J′ second-type auxiliary bits, where reliabilityof any one of the K′ subchannels is greater than or equal to reliabilityof any one of remaining M−K′ subchannels; performing, by the sendingdevice, polar encoding on a to-be-encoded sequence based on positions ofsubchannels corresponding to the J first-type auxiliary bits, positionsof subchannels corresponding to the J′ second-type auxiliary bits, andpositions of subchannels corresponding to the K information bits; andsending, by the sending device, an encoded sequence.

In this solution, the J′ second-type auxiliary bits are selecteddirectly based on reliability ranking or subchannel number ranking or aprestored table, so that rapid locating can be implemented, and anencoding delay and a decoding delay can be effectively reduced.

In a possible implementation, when N>M, the method further includes:selecting, by the sending device, subchannels corresponding to N−M bitsin a mother code sequence as punctured subchannels.

In a possible implementation,

the quantity J′ of second-type auxiliary bits is preconfigured; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in the K′ subchannels, or first J′ subchannels thatare not punctured subchannels and that are ranked in descending order ofreliability in the K′ subchannels. This method is simpler and moreintuitive.

In a possible implementation, the sending device sequentially selects,based on K′ and N, J′ numbers that are not of punctured subchannels froma prestored table in a left-to-right order, where subchannelscorresponding to the J′ numbers are used to transmit the J′ second-typeauxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 1 or some or all content of Table 2.

In this table lookup manner, overheads of real-time row weightcalculation and reliability calculation are avoided, the encodingprocess is accelerated, and calculation overheads and a delay arereduced.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a row weight W_(min) in the K′subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a row weight W_(min) in the K′subchannels. W_(min) is a minimum row weight of the K′ subchannels.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a Hamming weight H_(min) in theK′ subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a Hamming weight H_(min) in the K′subchannels. H_(min) is a minimum Hamming weight of the K′ subchannels,and the minimum Hamming weight H_(min)=log₂ W_(min).

In a possible implementation, W_(min)=2^(t+D), where D is a constant,t=1, 2, . . . , or T, t is a row weight transition point indexcorresponding to K′, K′ meets K_(t)≤K′<K_(t−1), K_(t) is a subchannelquantity corresponding to a t^(th) row weight transition point, and T isa positive integer.

In a possible implementation, D=0.

In a possible implementation, the sending device selects the row weighttransition point index corresponding to K′ from a prestored table basedon K′ and N. The prestored table is used to represent a correspondencebetween the row weight transition point index and the T row weighttransition points in different mother code lengths, and K′ meetsK_(t)≤K′<K_(t−1).

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, the sending device determines W_(min)based on K′ and N. Specifically, the sending device selects W_(min)corresponding to K′ from a prestored table based on K′ and N. Theprestored table is used to represent a correspondence between W_(min),the T row weight transition points in the different mother code lengths,and subchannel quantities that are in one-to-one correspondence with theT row weight transition points, K′ meets K_(t)≤K′<K_(t−1), K_(t) is thesubchannel quantity corresponding to the t^(th) row weight transitionpoint, t=1, 2, . . . , or T, t is the row weight transition point indexcorresponding to K′, and T is a positive integer.

In a possible implementation, the prestored table is some or all contentof Table 4.

In a possible implementation, after W_(min) is determined, the methodfurther includes: dividing a sequence corresponding to a row weightW_(min) in prestored position number sequences of a mother code lengthN_(max) that are corresponding to different row weights by N_(max)/N,reserving an integer quotient, and sequentially selecting J′ positionnumbers that are not of punctured subchannels from the reserved integerquotient in a left-to-right order, where subchannels corresponding tothe J′ position numbers are used to transmit the J′ second-typeauxiliary bits.

In a possible implementation, after W_(min) is determined, the methodfurther includes: reserving position numbers less than or equal to N fora sequence corresponding to a row weight W_(min)×N_(max)/N in prestoredposition number sequences of a mother code length N_(max) that arecorresponding to different row weights, and sequentially selecting J′position numbers that are not of punctured subchannels from the reservedposition numbers less than or equal to N in a left-to-right order, wheresubchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 5, or some or all content of Table 6.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 7, or some or all content of Table 8.

In a possible implementation, the sending device selects a row weighttransition point index t corresponding to K′ from a prestored tablebased on K′ and N. The prestored table is used to represent acorrespondence between the row weight transition point index and the Trow weight transition points in different mother code lengths. T is apositive integer, and K′ meets K_(t)≤K′<K_(t−1). The sending deviceselects prestored position number sequences of a mother code lengthN_(max) that are corresponding to different indexes, divides theposition number sequences by N_(max)/N, reserves an integer quotient,and sequentially selects J′ position numbers that are not of puncturedsubchannels from the reserved integer quotient in a left-to-right order.Subchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table9, or some or all content of Table 10.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table11, or some or all content of Table 12.

In a possible implementation, subchannel numbers corresponding to the J′position numbers are N−X, and X is the J′ position numbers.

In a possible implementation, the first-type auxiliary bits are CRCbits.

In a possible implementation, the second-type auxiliary bits is PC bits.

A second aspect of this application provides a decoding method. A mothercode length used in a decoding process is N, a code rate is R, a codelength obtained after encoding is M, a quantity of information bits isK, a quantity of first-type auxiliary bits is J, a quantity ofsecond-type auxiliary bits is J′, K+J+J′=K′, and the decoding methodincludes:

determining, by a receiving device, positions of the information bits,the first-type auxiliary bits, and the second-type auxiliary bits basedon the mother code length N, the code length M, and the quantity K ofinformation bits, where N is an integral power of 2, and M and K arepositive integers; and

decoding a to-be-decoded sequence based on positions of the informationbits, punctured bits, the first-type auxiliary bits, and the second-typeauxiliary bits.

In a possible implementation, when N>M, the method further includes:selecting, by the receiving device, subchannels corresponding to N−Mbits in a mother code sequence as punctured subchannels.

In a possible implementation,

the quantity J′ of second-type auxiliary bits is preconfigured; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in the K′ subchannels, or first J′ subchannels thatare not punctured subchannels and that are ranked in descending order ofreliability in the K′ subchannels.

In a possible implementation, the receiving device sequentially selects,based on K′ and N, J′ numbers that are not of punctured subchannels froma prestored table in a left-to-right order, where subchannelscorresponding to the J′ numbers are used to transmit the J′ second-typeauxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 1 or some or all content of Table 2.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a row weight W_(min) in the K′subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a row weight W_(min) in the K′subchannels, where W_(min) is a minimum row weight of the K′subchannels.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a Hamming weight H_(min) in theK′ subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a Hamming weight H_(min) in the K′subchannels. H_(min) is a minimum Hamming weight of the K′ subchannels,and the minimum Hamming weight H_(min)=log₂ W_(min).

In a possible implementation, W_(min)=2^(t+D), where D is a constant,t=1, 2, . . . , or T, t is a row weight transition point indexcorresponding to K′, K′ meets K_(t)≤K′<K_(t−1), K_(t) is a subchannelquantity corresponding to a t^(th) row weight transition point, and T isa positive integer.

In a possible implementation, D=0.

In a possible implementation, the receiving device selects the rowweight transition point index corresponding to K′ from a prestored tablebased on K′ and N. The prestored table is used to represent acorrespondence between the row weight transition point index and the Trow weight transition points in different mother code lengths, and K′meets K_(t)≤K′<K_(t−1).

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, the receiving device determines W_(min)based on K′ and N. Specifically, the receiving device selects W_(min)corresponding to K′ from a prestored table based on K′ and N. Theprestored table is used to represent a correspondence between W_(min),the T row weight transition points in the different mother code lengths,and subchannel quantities that are in one-to-one correspondence with theT row weight transition points, K′ meets K_(t)≤K′<K_(t−1), K_(t) is thesubchannel quantity corresponding to the t^(th) row weight transitionpoint, t=1, 2, . . . , or T, t is the row weight transition point indexcorresponding to K′, and T is a positive integer.

In a possible implementation, the prestored table is some or all contentof Table 4.

In a possible implementation, after W_(min) is determined, the methodfurther includes: dividing a sequence corresponding to a row weightW_(min) in prestored position number sequences of a mother code lengthN_(max) that are corresponding to different row weights by N_(max)/N,reserving an integer quotient, and sequentially selecting J′ positionnumbers that are not of punctured subchannels from the reserved integerquotient in a left-to-right order, where subchannels corresponding tothe J′ position numbers are used to transmit the J′ second-typeauxiliary bits.

In a possible implementation, after W_(min) is determined, the methodfurther includes: reserving position numbers less than or equal to N fora sequence corresponding to a row weight W_(min)×N_(max)/N in prestoredposition number sequences of a mother code length N_(max) that arecorresponding to different row weights, and sequentially selecting J′position numbers that are not of punctured subchannels from the reservedposition numbers less than or equal to N in a left-to-right order, wheresubchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 5, or some or all content of Table 6.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 7, or some or all content of Table 8.

In a possible implementation, the receiving device selects a row weighttransition point index t corresponding to K′ from a prestored tablebased on K′ and N. The prestored table is used to represent acorrespondence between the row weight transition point index and the Trow weight transition points in different mother code lengths, T is apositive integer, and K′ meets K_(t)≤K′<K_(t−1). The receiving deviceselects prestored position number sequences of a mother code lengthN_(max) that are corresponding to different indexes, divides theposition number sequences by N_(max)/N, reserves an integer quotient,and sequentially selects J′ position numbers that are not of puncturedsubchannels from the reserved integer quotient in a left-to-right order,where subchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table9, or some or all content of Table 10.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table11, or some or all content of Table 12.

In a possible implementation, subchannel numbers corresponding to the J′position numbers are N−X, and X is the J′ position numbers.

In a possible implementation, the first-type auxiliary bits are CRCbits.

In a possible implementation, the second-type auxiliary bits are PCbits.

A third aspect of this application provides an encoding apparatus. Amother code length used in an encoding process is N, a code rate is R, acode length obtained after encoding is M, a quantity of information bitsis K, a quantity of first-type auxiliary bits is J, a quantity ofsecond-type auxiliary bits is J′, K+J+J′=K′, and the encoding apparatusincludes:

an encoding module 41, configured to perform polar encoding on ato-be-encoded sequence, where a mother code length of a polar code is N,and the to-be-encoded sequence includes frozen bits, first-typeauxiliary bits, second-type auxiliary bits, and information bits;

a determining module 42, configured to determine subchannelscorresponding to the frozen bits, the first-type auxiliary bits, thesecond-type auxiliary bits, and the information bits, where thedetermining module 42 is further configured to determine values of thefirst-type auxiliary bits and the second-type auxiliary bits; and

a sending module 43, configured to send an encoded sequence.

In a possible implementation, when N>M, the determining module selectssubchannels corresponding to N−M bits in a mother code sequence aspunctured subchannels.

In a possible implementation,

the quantity J′ of second-type auxiliary bits is preconfigured; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in the K′ subchannels, or first J′ subchannels thatare not punctured subchannels and that are ranked in descending order ofreliability in the K′ subchannels.

In a possible implementation, the determining module sequentiallyselects, based on K′ and N, J′ numbers that are not of puncturedsubchannels from a prestored table in a left-to-right order, wheresubchannels corresponding to the J′ numbers are used to transmit the J′second-type auxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 1 or some or all content of Table 2.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a row weight W_(min) in the K′subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a row weight W_(min) in the K′subchannels. W_(min) is a minimum row weight of the K′ subchannels.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a Hamming weight H_(min) in theK′ subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a Hamming weight H_(min) in the K′subchannels. H_(min) is a minimum Hamming weight of the K′ subchannels,and the minimum Hamming weight H_(min)=log₂ W_(min).

In a possible implementation, W_(min)=2^(t+D), where D is a constant,t=1, 2, . . . , or T, t is a row weight transition point indexcorresponding to K′, K′ meets K_(t)≤K′<K_(t−1), K_(t) is a subchannelquantity corresponding to a t^(th) row weight transition point, and T isa positive integer.

In a possible implementation, D=0.

In a possible implementation, the determining module selects the rowweight transition point index corresponding to K′ from a prestored tablebased on K′ and N. The prestored table is used to represent acorrespondence between the row weight transition point index and the Trow weight transition points in different mother code lengths, and K′meets K_(t)≤K′<K_(t−1).

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, the determining module determines W_(min)based on K′ and N. Specifically, the determining module selects W_(min)corresponding to K′ from a prestored table based on K′ and N, where theprestored table is used to represent a correspondence between W_(min),the T row weight transition points in the different mother code lengths,and subchannel quantities that are in one-to-one correspondence with theT row weight transition points, K′ meets K_(t)≤K′<K_(t−1), K_(t) is thesubchannel quantity corresponding to the t^(th) row weight transitionpoint, t=1, 2, . . . , or T, t is the row weight transition point indexcorresponding to K′, and T is a positive integer.

In a possible implementation, the prestored table is some or all contentof Table 4.

In a possible implementation, after determining W_(min), the determiningmodule divides a sequence corresponding to a row weight W_(min) inprestored position number sequences of a mother code length N_(max) thatare corresponding to different row weights by N_(max)/N, reserves aninteger quotient, and sequentially selects J′ position numbers that arenot of punctured subchannels from the reserved integer quotient in aleft-to-right order, where subchannels corresponding to the J′ positionnumbers are used to transmit the J′ second-type auxiliary bits.

In a possible implementation, after determining W_(min), the determiningmodule reserves position numbers less than or equal to N for a sequencecorresponding to a row weight W_(min)×N_(max)/N in prestored positionnumber sequences of a mother code length N_(max) that are correspondingto different row weights, and sequentially selects J′ position numbersthat are not of punctured subchannels from the reserved position numbersless than or equal to N in a left-to-right order, where subchannelscorresponding to the J′ position numbers are used to transmit the J′second-type auxiliary bits.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 5, or some or all content of Table 6.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 7, or some or all content of Table 8.

In a possible implementation, the determining module selects a rowweight transition point index t corresponding to K′ from a prestoredtable based on K′ and N. The prestored table is used to represent acorrespondence between the row weight transition point index and the Trow weight transition points in different mother code lengths, T is apositive integer, and K′ meets K_(t)≤K′<K_(t−1). The determining moduleselects prestored position number sequences of a mother code lengthN_(max) that are corresponding to different indexes, divides theposition number sequences by N_(max)/N, reserves an integer quotient,and sequentially selects J′ position numbers that are not of puncturedsubchannels from the reserved integer quotient in a left-to-right order.Subchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table9, or some or all content of Table 10.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table11, or some or all content of Table 12.

In a possible implementation, subchannel numbers corresponding to the J′position numbers are N−X, and X is the J′ position numbers.

In a possible implementation, the first-type auxiliary bits are CRCbits.

In a possible implementation, the second-type auxiliary bits are PCbits.

A fourth aspect of this application provides a receiving apparatus. Amother code length used in a decoding process is N, a code rate is R, acode length obtained after encoding is M, a quantity of information bitsis K, a quantity of first-type auxiliary bits is J, a quantity ofsecond-type auxiliary bits is J′, K+J+J′=K′, and the receiving apparatusincludes:

an obtaining module 51, configured to obtain a to-be-decoded sequence;

a determining module 52, configured to determine subchannelscorresponding to frozen bits, first-type auxiliary bits, second-typeauxiliary bits, punctured bits, and information bits; and

a decoding module 53, configured to perform polar decoding on thereceived to-be-decoded sequence to obtain a decoded sequence.

In a possible implementation, when N>M, the determining module selectssubchannels corresponding to N−M bits in a mother code sequence aspunctured subchannels.

In a possible implementation,

the quantity J′ of second-type auxiliary bits is preconfigured; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in the K′ subchannels, or first J′ subchannels thatare not punctured subchannels and that are ranked in descending order ofreliability in the K′ subchannels.

In a possible implementation, the determining module sequentiallyselects, based on K′ and N, J′ numbers that are not of puncturedsubchannels from a prestored table in a left-to-right order, wheresubchannels corresponding to the J′ numbers are used to transmit the J′second-type auxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 1 or some or all content of Table 2.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a row weight W_(min) in the K′subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a row weight W_(min) in the K′subchannels. W_(min) is a minimum row weight of the K′ subchannels.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a Hamming weight H_(min) in theK′ subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a Hamming weight H_(min) in the K′subchannels, H_(min) is a minimum Hamming weight of the K′ subchannels,and the minimum Hamming weight H_(min)=log₂ W_(min).

In a possible implementation, W_(min)=2^(t+D), where D is a constant,t=1, 2, . . . , or T, t is a row weight transition point indexcorresponding to K′, K′ meets K_(t)≤K′<K_(t−1), K_(t) is a subchannelquantity corresponding to a t^(th) row weight transition point, and T isa positive integer.

In a possible implementation, D=0.

In a possible implementation, the determining module selects the rowweight transition point index corresponding to K′ from a prestored tablebased on K′ and N. The prestored table is used to represent acorrespondence between the row weight transition point index and the Trow weight transition points in different mother code lengths, and K′meets K_(t)≤K′<K_(t−1).

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, the determining module determines W_(min)based on K′ and N. Specifically, the determining module selects W_(min)corresponding to K′ from a prestored table based on K′ and N, where theprestored table is used to represent a correspondence between W_(min),the T row weight transition points in the different mother code lengths,and subchannel quantities that are in one-to-one correspondence with theT row weight transition points, K′ meets K_(t)≤K′<K_(t−1), K_(t) is thesubchannel quantity corresponding to the t^(th) row weight transitionpoint, t=1, 2, . . . , or T, t is the row weight transition point indexcorresponding to K′, and T is a positive integer.

In a possible implementation, the prestored table is some or all contentof Table 4.

In a possible implementation, after determining W_(min), the determiningmodule divides a sequence corresponding to a row weight W_(min) inprestored position number sequences of a mother code length N_(max) thatare corresponding to different row weights by N_(max)/N. The determiningmodule reserves an integer quotient, and sequentially selects J′position numbers that are not of punctured subchannels from the reservedinteger quotient in a left-to-right order, where subchannelscorresponding to the J′ position numbers are used to transmit the J′second-type auxiliary bits.

In a possible implementation, after determining W_(min), the determiningmodule reserves position numbers less than or equal to N for a sequencecorresponding to a row weight W_(min)×N_(max)/N in prestored positionnumber sequences of a mother code length N_(max) that are correspondingto different row weights, and sequentially selects J′ position numbersthat are not of punctured subchannels from the reserved position numbersless than or equal to N in a left-to-right order, where subchannelscorresponding to the J′ position numbers are used to transmit the J′second-type auxiliary bits.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 5, or some or all content of Table 6.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 7, or some or all content of Table 8.

In a possible implementation, the determining module selects a rowweight transition point index t corresponding to K′ from a prestoredtable based on K′ and N. The prestored table is used to represent acorrespondence between the row weight transition point index and the Trow weight transition points in different mother code lengths, T is apositive integer, and K′ meets K_(t)≤K′<K_(t−1). The determining moduleselects prestored position number sequences of a mother code lengthN_(max) that are corresponding to different indexes, divides theposition number sequences by N_(max)/N, reserves an integer quotient,and sequentially selects J′ position numbers that are not of puncturedsubchannels from the reserved integer quotient in a left-to-right order,where subchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table9, or some or all content of Table 10.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table11, or some or all content of Table 12.

In a possible implementation, subchannel numbers corresponding to the J′position numbers are N−X, and X is the J′ position numbers.

In a possible implementation, the first-type auxiliary bits are CRCbits.

In a possible implementation, the second-type auxiliary bits are PCbits.

A fifth aspect of this application provides an encoding apparatus. Amother code length used in an encoding process is N, a code rate is R, acode length obtained after encoding is M, a quantity of information bitsis K, a quantity of first-type auxiliary bits is J, a quantity ofsecond-type auxiliary bits is J′, K+J+J′=K′, and the encoding apparatusincludes:

a memory 1101, configured to store an execution instruction; and

a processor 1102, configured to execute the execution instruction storedin the memory, where the processor is configured to perform polarencoding on a to-be-encoded sequence, where a mother code length of apolar code is N, and the to-be-encoded sequence includes frozen bits,first-type auxiliary bits, second-type auxiliary bits, and informationbits, where

the processor is further configured to determine subchannelscorresponding to the frozen bits, the first-type auxiliary bits, thesecond-type auxiliary bits, and the information bits; and the processoris further configured to determine values of the first-type auxiliarybits and the second-type auxiliary bits.

In a possible implementation, when the processor is implemented byhardware, the memory may not be required.

In a possible implementation, a transmitter of the encoding apparatus isconfigured to send an encoded sequence.

In a possible implementation, when N>M, the processor selectssubchannels corresponding to N−M bits in a mother code sequence aspunctured subchannels.

In a possible implementation, the quantity J′ of second-type auxiliarybits is preconfigured; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K−J,K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in the K′ subchannels, or first J′ subchannels thatare not punctured subchannels and that are ranked in descending order ofreliability in the K′ subchannels.

In a possible implementation, the processor sequentially selects, basedon K′ and N, J′ numbers that are not of punctured subchannels from aprestored table in a left-to-right order, where subchannelscorresponding to the J′ numbers are used to transmit the J′ second-typeauxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 1 or some or all content of Table 2.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a row weight W_(min) in the K′subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a row weight W_(min) in the K′subchannels, where W_(min) is a minimum row weight of the K′subchannels.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a Hamming weight H_(min) in theK′ subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are or first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a Hamming weight H_(min) in the K′subchannels. H_(min) is a minimum Hamming weight of the K′ subchannels,and the minimum Hamming weight H_(min)=log₂ W_(min).

In a possible implementation, W_(min)=2^(t+D), where D is a constant,t=1, 2, . . . , or T, t is a row weight transition point indexcorresponding to K′, K′ meets K_(t)≤K′<K_(t−1), K_(t) is a subchannelquantity corresponding to a t^(th) row weight transition point, and T isa positive integer.

In a possible implementation, D=0.

In a possible implementation, the processor selects the row weighttransition point index corresponding to K′ from a prestored table basedon K′ and N. The prestored table is used to represent a correspondencebetween the row weight transition point index and the T row weighttransition points in different mother code lengths, and K′ meetsK_(t)≤K′<K_(t−1).

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, the processor determines W_(min) based onK′ and N. Specifically, the processor selects W_(min) corresponding toK′ from a prestored table based on K′ and N. The prestored table is usedto represent a correspondence between W_(min), the T row weighttransition points in the different mother code lengths, and subchannelquantities that are in one-to-one correspondence with the T row weighttransition points, K′ meets K_(t)≤K′<K_(t−1), K_(t) is the subchannelquantity corresponding to the t^(th) row weight transition point, t=1,2, . . . , or T, t is the row weight transition point indexcorresponding to K′, and T is a positive integer.

In a possible implementation, the prestored table is some or all contentof Table 4.

In a possible implementation, after determining W_(min), the processordivides a sequence corresponding to a row weight W_(min) in prestoredposition number sequences of a mother code length N_(max) that arecorresponding to different row weights by N_(max)/N, reserves an integerquotient, and sequentially selects J′ position numbers that are not ofpunctured subchannels from the reserved integer quotient in aleft-to-right order, where subchannels corresponding to the J′ positionnumbers are used to transmit the J′ second-type auxiliary bits.

In a possible implementation, after determining W_(min), the processorreserves position numbers less than or equal to N for a sequencecorresponding to a row weight W_(min)×N_(max)/N in prestored positionnumber sequences of a mother code length N_(max) that are correspondingto different row weights, and sequentially selects J′ position numbersthat are not of punctured subchannels from the reserved position numbersless than or equal to N in a left-to-right order, where subchannelscorresponding to the J′ position numbers are used to transmit the J′second-type auxiliary bits.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 5, or some or all content of Table 6.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 7, or some or all content of Table 8.

In a possible implementation, the processor selects a row weighttransition point index t corresponding to K′ from a prestored tablebased on K′ and N. The prestored table is used to represent acorrespondence between the row weight transition point index and the Trow weight transition points in different mother code lengths, T is apositive integer, and K′ meets K_(t)≤K′<K_(t−1). The processor selectsprestored position number sequences of a mother code length N_(max) thatare corresponding to different indexes, divides the position numbersequences by N_(max)/N, reserves an integer quotient, and sequentiallyselects J′ position numbers that are not of punctured subchannels fromthe reserved integer quotient in a left-to-right order, wheresubchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table9, or some or all content of Table 10.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table11, or some or all content of Table 12.

In a possible implementation, subchannel numbers corresponding to the J′position numbers are N−X, and X is the J′ position numbers.

In a possible implementation, the first-type auxiliary bits are CRCbits.

In a possible implementation, the second-type auxiliary bits are PCbits.

A sixth aspect of this application provides a decoding apparatus. Amother code length used in a decoding process is N, a code rate is R, acode length obtained after encoding is M, a quantity of information bitsis K, a quantity of first-type auxiliary bits is J, a quantity ofsecond-type auxiliary bits is J′, K+J+J′=K′, and the decoding apparatusincludes:

a memory 1201, configured to store an execution instruction, where thememory may be a flash (flash memory); and

a processor 1202, configured to execute the execution instruction storedin the memory, where the processor is configured to determinesubchannels corresponding to frozen bits, first-type auxiliary bits,second-type auxiliary bits, punctured bits, and information bits, wherethe processor is further configured to perform polar decoding on areceived to-be-decoded sequence to obtain a decoded sequence.

In a possible implementation, when the processor is implemented byhardware, the memory may not be required.

In a possible implementation, the apparatus further includes a receiver,configured to receive a to-be-decoded signal or the to-be-decodedsequence.

In a possible implementation, when N>M, the processor selectssubchannels corresponding to N−M bits in a mother code sequence aspunctured subchannels.

In a possible implementation,

the quantity J′ of second-type auxiliary bits is preconfigured; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(N−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(N−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(M−K−J)+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer; or

the quantity J′ of second-type auxiliary bits meetsJ′=integer(log₂(min(M−K−J,K))+C), where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in the K′ subchannels, or first J′ subchannels thatare not punctured subchannels and that are ranked in descending order ofreliability in the K′ subchannels.

In a possible implementation, the processor sequentially selects, basedon K′ and N, J′ numbers that are not of punctured subchannels from aprestored table in a left-to-right order, where subchannelscorresponding to the J′ numbers are used to transmit the J′ second-typeauxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 1 or some or all content of Table 2.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a row weight W_(min) in the K′subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a row weight W_(min) in the K′subchannels. W_(min) is a minimum row weight of the K′ subchannels.

In a possible implementation, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofsubchannel numbers in subchannels with a Hamming weight H_(min) in theK′ subchannels. Alternatively, the subchannels corresponding to the J′second-type auxiliary bits are first J′ subchannels that are notpunctured subchannels and that are ranked in descending order ofreliability in subchannels with a Hamming weight H_(min) in the K′subchannels. H_(min) is a minimum Hamming weight of the K′ subchannels,and the minimum Hamming weight H_(min)=log₂ W_(min).

In a possible implementation, W_(min)=2^(t+D), where D is a constant,t=1, 2, . . . , or T, t is a row weight transition point indexcorresponding to K′, K′ meets K_(t)≤K′<K_(t−1), K_(t) is a subchannelquantity corresponding to a t^(th) row weight transition point, and T isa positive integer.

In a possible implementation, D=0.

In a possible implementation, the processor selects the row weighttransition point index corresponding to K′ from a prestored table basedon K′ and N. The prestored table is used to represent a correspondencebetween the row weight transition point index and the T row weighttransition points in different mother code lengths, and K′ meetsK_(t)≤K′<K_(t−1).

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, the processor determines W_(min) based onK′ and N. Specifically, the processor selects W_(min) corresponding toK′ from a prestored table based on K′ and N. The prestored table is usedto represent a correspondence between W_(min), the T row weighttransition points in the different mother code lengths, and subchannelquantities that are in one-to-one correspondence with the T row weighttransition points, K′ meets K_(t)≤K′<K_(t−1), K_(t) is the subchannelquantity corresponding to the t^(th) row weight transition point, t=1,2, . . . , or T, t is the row weight transition point indexcorresponding to K′, and T is a positive integer.

In a possible implementation, the prestored table is some or all contentof Table 4.

In a possible implementation, after determining W_(min), the processordivides a sequence corresponding to a row weight W_(min) in prestoredposition number sequences of a mother code length N_(max) that arecorresponding to different row weights by N_(max)/N, reserves an integerquotient, and sequentially selects J′ position numbers that are not ofpunctured subchannels from the reserved integer quotient in aleft-to-right order, where subchannels corresponding to the J′ positionnumbers are used to transmit the J′ second-type auxiliary bits.

In a possible implementation, after determining W_(min), the processorreserves position numbers less than or equal to N for a sequencecorresponding to a row weight W_(min)×N_(max)/N in prestored positionnumber sequences of a mother code length N_(max) that are correspondingto different row weights. The processor sequentially selects J′ positionnumbers that are not of punctured subchannels from the reserved positionnumbers less than or equal to N in a left-to-right order, wheresubchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 5, or some or all content of Table 6.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different row weights are some or all content ofTable 7, or some or all content of Table 8.

In a possible implementation, the processor selects a row weighttransition point index t corresponding to K′ from a prestored tablebased on K′ and N. The prestored table is used to represent acorrespondence between the row weight transition point index and the Trow weight transition points in different mother code lengths, T is apositive integer, and K′ meets K_(t)≤K′<K_(t−1). The processor selectsprestored position number sequences of a mother code length N_(max) thatare corresponding to different indexes, divides the position numbersequences by N_(max)/N, reserves an integer quotient, and sequentiallyselects J′ position numbers that are not of punctured subchannels fromthe reserved integer quotient in a left-to-right order, wheresubchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In a possible implementation, the prestored table is some or all contentof Table 3.

In a possible implementation, N_(max)=512, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table9, or some or all content of Table 10.

In a possible implementation, N_(max)=1024, and the prestored positionnumber sequences of the mother code length N_(max) that arecorresponding to the different indexes are some or all content of Table11, or some or all content of Table 12.

In a possible implementation, subchannel numbers corresponding to the J′position numbers are N−X, and X is the J′ position numbers.

In a possible implementation, the first-type auxiliary bit are CRC bits.

In a possible implementation, the second-type auxiliary bits are PCbits.

A seventh aspect of this application provides a computer readablestorage medium. The computer readable storage medium stores acomputer-executable instruction, and when at least one processor of asending device executes the computer-executable instruction, the sendingdevice executes the data encoding method provided in the first aspect orthe various implementations of the first aspect.

An eighth aspect of this application provides a computer readablestorage medium. The computer readable storage medium stores acomputer-executable instruction, and when at least one processor of areceiving device executes the computer-executable instruction, thereceiving device executes the data decoding method provided in thesecond aspect or the various implementations of the second aspect.

A ninth aspect of this application provides a computer program product.The computer program product includes a computer-executable instruction,and the computer-executable instruction is stored in a computer readablestorage medium. At least one processor of a sending device may read thecomputer-executable instruction from the computer readable storagemedium, and the at least one processor executes the computer-executableinstruction, so that the sending device implements the data encodingmethod provided in the first aspect or the various implementations ofthe first aspect.

A tenth aspect of this application provides a computer program product.The computer program product includes a computer-executable instruction,and the computer-executable instruction is stored in a computer readablestorage medium. At least one processor of a receiving device may readthe computer-executable instruction from the computer readable storagemedium, and the at least one processor executes the computer-executableinstruction, so that the receiving device implements the data decodingmethod provided in the second aspect or the various implementations ofthe second aspect.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of a communication system in which dataencoding method or data decoding method according to embodiments of thisapplication can be applied;

FIG. 2 is a flowchart of a data encoding method according to anembodiment of this application;

FIG. 3 is a flowchart of a data decoding method according to anembodiment of this application;

FIG. 4 is a block diagram of an encoding apparatus according to anembodiment of this application;

FIG. 5 is a block diagram of a receiving apparatus according to anembodiment of this application;

FIG. 6 is a simplified structural diagram of an encoding entityapparatus according to an embodiment of this application; and

FIG. 7 is a simplified structural diagram of a decoding entity apparatusaccording to an embodiment this application.

DESCRIPTION OF EMBODIMENTS

Generally, a CRC bit may be considered as a first-type auxiliary bit,and a PC bit and the like are considered as second-type auxiliary bits.In some cases, some CRC bits may also be considered as second-typeauxiliary bits, and this is not limited herein.

To avoid a delay caused in determining an auxiliary bit position whenminimum row weight W_(min) is determined through real-time calculationand searching, the embodiments of this application provide a method fordetermining an auxiliary bit position based on a prestored table. Inparticular, an auxiliary bit position can be selected based onreliabilities (including polarization weight, Gaussian approximation,and other types of reliability) or based on subchannel sequence numbers.In specific implementation, optionally, an auxiliary bit position may bedetermined based on a minimum Hamming weight. The minimum Hamming weightH_(min) may be calculated by using the W_(min), to be specific,H_(min)=log₂ W_(min), and therefore the two are essentially equivalent.In this application, the minimum row weight is used for description, butcertainly, the minimum Hamming weight can also be used in a similarmanner.

The technical solutions in embodiments of this application can beapplied to various communications systems, such as WiFi systems and thefifth generation (5G) communications systems currently in development.FIG. 1 is a schematic diagram of a communication system in which a datasending method or a data receiving method according to embodiments ofthis application can be applied. As shown in FIG. 1, for a cellularnetwork, the system includes a network device (such as a base station)and a terminal device, or, for a WiFi network, the system includes aWiFi access point and a WiFi terminal. Quantity of network devices andquantity of terminals are not limited. When the network device transmitsa downlink signal to the terminal, polar code or other channel encodingprocesses may be performed. Polar code may also be used in uplink signaltransmission. The subsequently provided method can be used in bothuplink data transmission and downlink data transmission.

In the foregoing network architecture, the network device provides acommunication service for a terminal device. The network device may be abase station on a network side, or other devices that can provide basestation functions. In a wireless network, a base station is alsoreferred to as a radio access network (AN) device, and is a device thatconnects the terminal to the wireless network. In the foregoingarchitecture, the base station may be an evolved NodeB (eNB or eNodeB),a relay station, or an access point in a Long Term Evolution (LTE)network, or a base station or the like in a 5G network. The terminal isa device that performs uplink and downlink data interactions with thenetwork device from a user's side. For example, the terminal may be amobile phone or a tablet computer. In addition, in a device-to-device(D2D) communication, the network device may also be a terminal thatundertakes a base station function. There is no limit herein.

FIG. 2 is a flowchart of an encoding method according to an embodimentof this application. Based on the schematic network diagram shown inFIG. 1, both a network device and a terminal may be used as a sendingdevice for the method shown in FIG. 2. The method specifically includesthe following steps.

210. Determine positions of information bits, punctured bits, CRC bits,and PC bits in a to-be-encoded sequence based on a mother code length N,a code length M, and an information bit quantity K, where N is anintegral power of 2, and M and K are positive integers. Generally, a CRCbit is an example of a first-type auxiliary bit, and a PC bit is anexample of the second-type auxiliary bit herein.

It should be noted that in some cases, the sending device may determinethe positions of these bits based on N, M, and a code rate R, where Rmeets R=K/M.

Step 210 may be further divided into the following substeps:

211. Obtain a reliability order of N subchannels corresponding to N bitsin a binary row vector u₁ ^(N) (also referred to as the to-be-encodedsequence). This is done by: (a) Calculate or retrieve reliabilities ofthe subchannels; and (b) rank the subchannels by reliability to obtain areliability ranking sequence Q, where Q is a subchannel number sequenceobtained by ranking the reliability in ascending order. Certainly, Q mayalternatively be a subchannel number sequence obtained by ranking thereliability in descending order. Generally, ranking in ascending orderis used as an example for description in this application.

212. When N>M, N−M bits in the to-be-encoded sequence are punctured.Subchannels corresponding to N−M punctured bits are selected aspunctured subchannels. This step is performed only when N>M. When N=M,this step may be skipped.

213. (a) Calculate or retrieve a parameter W_(min). In this embodiment,W_(min) is a minimum row weight of rows in the polar generator matrixG_(N) that correspond to K′ bits (including information bits, CRC bits,and PC bits) in the to-be-encoded sequence, and K′=K+J+J′; and (b)determine a quantity J of CRC bits and a quantity J′ of PC bits bycalculation or retrieving.

214. Determine positions of the PC bits and the CRC bits in theto-be-encoded sequence.

215. Select K subchannels in descending order of reliability to transmitinformation bits, where in the to-be-encoded sequence, the K informationbits are placed at the positions corresponding to the selected Ksubchannels, the positions of the punctured bits, the PC bits, and theCRC bits are skipped.

216. Use all remaining unselected positions in the to-be-encodedsequence that correspond to non-punctured subchannels as positions offrozen bits.

It should be noted that step 215 and step 216 may be interchanged. Inother words, the positions of the frozen bits may be first selected,that is, N−K′ subchannels are selected in ascending order of reliabilityas subchannels of the frozen bits and the punctured bits, where thepositions of the information bits, the PC bits, and the CRC bits areskipped. Then, remaining positions of non-punctured subchannels are usedas the positions of the information bits, the PC bits, and the CRC bits.

220. Perform CRC encoding on to-be-encoded information bits to obtainCRC bits, and insert the obtained CRC bits into the positions selectedfor the CRC bits.

230. Calculate a value of the second-type auxiliary bits (for example,the PC bits) and insert the PC bits into the selected positions, toobtain the to-be-encoded sequence.

240. Perform Ankan polar encoding on the to-be-encoded sequence, toobtain an encoded sequence (i.e. the binary row vector x₁ ^(N)).

250. Perform rate matching based on the selected positions of thepunctured bits, to obtain a rate-matched encoded sequence. Therate-matched encoded sequence has a code length M. It should be notedthat the rate matching manners of puncturing and shortening are notdistinguished in this application, because a difference between the twois not related to the content of this application. For ease ofdescription, the punctured bits are uniformly used.

Corresponding to the encoding method of FIG. 2, FIG. 3 is a flowchart ofa polar decoding method according to an embodiments of this application.Based on the application scenario shown in FIG. 1, both the networkdevice and the terminal may be used as a receiving device for performingthe method as shown in FIG. 3. The method specifically includes thefollowing steps.

310. Determine positions of information bits, punctured bits, CRC bits,and PC bits in a to-be-decoded sequence, wherein the to-be-decodedsequence is obtained by rate-dematching a rate-matched encoded sequencebased on a mother code length N, a code length M, and an information bitquantity K, where N is an integral power of 2, and M and K are positiveintegers. Likewise, generally, a CRC bit is an example of a first-typeauxiliary bit, and a PC bit is an example of a second-type auxiliary bitherein.

It should be noted that in some cases, the receiving device maydetermine the positions of these bits based on N, M, and a code rate R,where R meets R=K/M.

Step 310 may be further divided into the following substeps:

311. Obtain a reliability order of N subchannels: (a) Calculate orretrieve a list of subchannel reliabilities; and (b) obtain areliability ranking sequence Q, where Q is a subchannel number sequenceobtained by ranking the reliability in ascending order. Certainly, Q mayalternatively be a subchannel number sequence obtained by ranking thereliability in descending order. Generally, ranking in ascending orderis used as an example for description in this application.

312. Select subchannels corresponding to N−M punctured bits as puncturedsubchannels. This step is performed only when N>M. When N=M, this stepmay be skipped. Similar to that at a transmit end, puncturing andshortening are not distinguished herein, and the punctured bits are usedfor description.

313. (a) Calculate or retrieve a parameter W_(min), where, in anembodiment, W_(min) is a minimum row weight of rows in the polargenerator matrix H that correspond to K′ bits (including informationbits, CRC bits, and PC bits, and K′=K+J+J′) in the to-be-encodedsequence; and (b) determine a quantity J of CRC bits and a quantity J′of PC bits by calculation or retrieving.

314. Determine positions of the PC bits and the CRC bits in theto-be-decoded sequence.

315. Select K subchannels in descending order of reliability, and toreceive the information bits in the positions corresponding to the Ksubchannels, where the positions of the punctured bit, the PC bit, andthe CRC bit are skipped.

316. Determine that all remaining unselected positions corresponding tothe non-punctured subchannels are positions of frozen bits.

Similar to the transmit end, step 315 and step 316 may be interchanged.In other words, the positions of the frozen bits are first determined,that is, N−K′ subchannels are selected in ascending order of reliabilityas subchannels of the frozen bits, where the positions of the puncturedbits, the PC bits, and the CRC bits are skipped. Remaining positions ofnon-punctured subchannels are determined as the positions of theinformation bits.

320. Perform Ankan polar decoding on the to-be-decoded sequence, andoutput a decoded sequence.

In step 213 and step 313, the quantity J of the CRC bits is usuallypreset. For example, J is usually 16 or 24. Certainly, J may also bedynamically specified. The quantity J′ of PC bits (or second-typeauxiliary bits) may be preconfigured, or may be calculated by using oneof the following formulas, where integer( ) represents a round-upoperation, a round-down operation, or a round-off operation, and C is aconstant integer, for example, C=0, 1, −1, 2, or −2:J′=integer(log₂(N−K)+C), orJ′=integer(log₂(N−K−J)+C), orJ′=integer(log₂(min(N−K,K))+C), orJ′=integer(log₂(min(N−K−J,K))+C), orJ′=integer(log₂(M−K)+C), orJ′=integer(log₂(M−K−J)+C), orJ′=integer(log₂(min(M−K,K))+C), orJ′=integer(log₂(min(M−K−J,K))+C).

Generally, the CRC bits are usually placed together with the informationbits, and occupy subchannels with high reliabilities. Therefore, in step214 and step 314, only the positions of the second-type auxiliary bitsmay be determined, and K+J subchannels are selected in step 215 and step315.

In steps 213, 214, 313, and 314, the following methods are used toobtain W_(min) and select positions of the J′ second-type auxiliary bits(for example, PC bits).

Method 1: Subchannels of the J′ second-type auxiliary bits are first J′subchannels that are not punctured subchannels and that are ranked indescending order of subchannel numbers in K′ subchannels. Alternatively,the subchannels of the J′ second-type auxiliary bits are first J′subchannels that are not punctured subchannels and that are ranked indescending order of reliabilities in K′ subchannels. In this manner,W_(min) does not need to be known. Therefore, optionally, (a) in step213 and 313 may be omitted.

Method 2: Subchannels of the J′ second-type auxiliary bits aredetermined based on N, K′, and a prestored table. Based on N and K′, alist of possible subchannel numbers corresponding to the second-typeauxiliary bits can be found in the prestored table, and J′ subchannelnumbers that are not of punctured subchannels are sequentially selectedin a left-to-right order. Certainly, the left-to-right order herein isrelated to a storage format in the table. To be specific, subchannelnumbers are ranked in descending order of reliability or in descendingorder of the subchannel numbers. If subchannel numbers are ranked inascending order, the J′ subchannel numbers need to be selected in aright-to-left order. However, this does not affect the essence of thepresent embodiments because subchannels that can be finally selected arecertainly consistent in the two orders. This is similar in the followingother tables, and details are not described again.

Table 1 and Table 2 show examples of possible second-type auxiliary bitsubchannel numbers in various mother code lengths less than or equal to1024. Table 1 is a correspondence table of N, K′, and possiblesecond-type auxiliary bit subchannel numbers ranked in descending orderof the subchannel numbers, and Table 2 is a correspondence table of N,K′, and possible second-type auxiliary bit subchannel numbers ranked indescending order of subchannel reliability. In the example of Table 1,if K′=20 and N=32, possible second-type auxiliary bit subchannel numbersare successively [24, 20, 18, 17, 12, 10, 9, 6, 5, 3]. If J′=3, and asubchannel 24 is a subchannel corresponding to a punctured bit, [20, 18,17] are the selected J′ subchannel numbers used to transmit thesecond-type auxiliary bits.

Method 3: It can be learned from a W_(min) distribution rule that whenthe mother code length N is given, W_(min) gradually decreases as K′increases. Because W_(min) is merely an integral power of 2, for a polarcode of the mother code length N, W_(min) is decreased only log₂N times,and only positions of K′ corresponding to log₂N transition points needto be prestored. Therefore, a row weight transition point K_(t)corresponding to K′ and an index t of the row weight transition pointmay be determined based on N, K′, and a prestored table, whereK_(t)≤K′<K_(t−1), and if K′≥K₁, t=1. The row weight transition pointK_(t) herein may be defined as follows: A row weight of a K_(t) ^(th)subchannel ranked in descending order in a sequence Q is ½ of a minimumrow weight of K_(t)−1 subchannels ranked in descending order in thesequence Q. W_(min) corresponding to K′ is calculated based on theobtained t: W_(min)=2^(t+D), where D is a constant, for example, D=0,0.5, or 1, and t=1, 2, . . . , or T.

For example, Table 3 shows row weight transition point distribution indifferent mother code lengths less than or equal to 1024. K′=20 and N=32are still used as an example. If D=0, a transition point number t=2.W_(min) may be obtained by using the following formula: W_(min)=2^(t)=4.Then first J′ subchannels that are not punctured subchannels and thatare ranked in descending order of subchannel numbers or first J′subchannels that are not punctured subchannels and that are ranked indescending order of reliability are selected from subchannels with a rowweight 4 in the K′ subchannels to transmit the J′ second-type auxiliarybits.

Method 4: Further, W_(min) is directly selected through table lookupbased on the method 3. The row weight transition point K_(t)corresponding to K′ and the corresponding W_(min) are determined basedon N, K′ and the prestored table. For example, Table 4 shows row weighttransition point distribution and corresponding W_(min) in differentmother code lengths less than or equal to 1024. Still in the example ofK′=20 and N=32, W_(min)=4, so that an online calculation step can beskipped, and a real-time calculation amount can be further reduced. Thenfirst J′ subchannels that are not punctured subchannels and that areranked in descending order of subchannel numbers or first J′ subchannelsthat are not punctured subchannels and that are ranked in descendingorder of reliability are selected from subchannels with a row weightW_(min) in the K′ subchannels to transmit the J′ second-type auxiliarybits.

Method 5: It can be learned by searching for a W_(min) distribution rulethat storage burden can be further reduced. Actually, only acorrespondence table between W_(min) and a possible second-typeauxiliary bit position number in a maximum mother code length needs tobe stored, and then a second-type auxiliary bit position is selectedaccording to a preset rule. For example, W_(min) corresponding to K′ isfirst obtained through real-time calculation or table lookup by usingone of the foregoing methods. Then, a sequence corresponding to a rowweight W_(min) in prestored position number sequences of a mother codelength N_(max) that are corresponding to different row weights isdivided by N_(max)/N, an integer quotient is reserved, and J′ positionnumbers that are not of punctured subchannels are sequentially selectedfrom the reserved integer quotient in a left-to-right order. Subchannelscorresponding to the J′ position numbers are used to transmit the J′second-type auxiliary bits. It should be noted that a position numbermeeting this rule is a reverse order of a subchannel number. Therefore,after a position number X is obtained, a subchannel number of asecond-type auxiliary bit needs to be obtained based on N−X.

For example, Table 5 shows a correspondence, in the case of N_(max)=512,between W_(min) and possible second-type auxiliary bit position numbersranked in descending order of subchannel numbers. K′=242 and N=256 areused as an example, and W_(min)=² may be obtained by searching Table 4.A position number sequence corresponding to W_(min)=2 in Table 5 is[256, 384, 448, 480, 496, 504, 508, 510, 511], and each element in thissequence is divided by N_(max)/N=512/256=2, so that [128, 192, 224, 240,248, 252, 254, 255, 255.5] can be obtained. A non-integer quotient isremoved and an integer quotient is reserved. In this case, obtainedcorresponding position numbers are [128, 192, 224, 240, 248, 252, 254,255], and a corresponding subchannel number sequence is [128, 64, 32,16, 8, 4, 2, 1]. It can be learned that this result is completelyconsistent with Table 1. Therefore, storage space can be moreeffectively saved in this manner. If J′=3 and a position number 192herein is a punctured subchannel, second-type auxiliary bit positionnumbers are X=[128, 224, 240], and subchannel numbers of the J′second-type auxiliary bits are N−X=[128, 32, 16].

Method 6: This method is similar to the principle of Method 5, but amanner of selecting a position number from a position number sequencecorresponding to N_(max) is slightly different. After W_(min) isdetermined, position numbers less than or equal to N are reserved for asequence corresponding to a row weight W_(min)×N_(max)/N in prestoredposition number sequences of a mother code length N_(max) that arecorresponding to different row weights, and J′ position numbers that arenot of punctured subchannels are sequentially selected from the reservedposition numbers less than or equal to N in a left-to-right order.Subchannels corresponding to the J′ position numbers are used totransmit the J′ second-type auxiliary bits.

In the example of Method 5, K′=242, N=256, and corresponding W_(min)=2.Table 5 is searched for a position number sequence withW_(min)=2×N_(max)/N=2×2=4, and the position number sequence is [128,192, 224, 240, 248, 252, 254, 255, 320, 352, 368, 376, 380, 382, 383,416, 432, 440, 444, 446, 447, 464, 472, 476, 478, 479, 488, 492, 494,495, 500, 502, 503, 506, 507, 509]. Position numbers greater than N=256are removed, and [128, 192, 224, 240, 248, 252 254, 255] can beobtained, and therefore a corresponding subchannel number sequence is[128, 64, 32, 16, 8, 4, 2, 1]. It can be learned that this result iscompletely consistent with Method 5 and Table 1. Therefore, storagespace can also be more effectively saved in this manner.

Similarly, Table 6 shows a correspondence, in the case of N_(max)=512,between W_(min) and possible second-type auxiliary bit position numbersranked in descending order of reliability. Table 7 shows acorrespondence, in the case of N_(max)=1024, between W_(min) andpossible second-type auxiliary bit position numbers ranked in descendingorder of subchannel numbers. Table 8 shows a correspondence, in the caseof N_(max)=1024, between W_(min) and possible second-type auxiliary bitposition numbers ranked in descending order of reliability. These tablesare also applicable to Method 5 and Method 6.

Method 7: Based on Method 5 and Method 6, it can be learned that W_(min)plays only a bridge function. In an actual system, position numbers ofthe J′ second-type auxiliary bits can be obtained without a need tocalculate or determine W_(min). Details are as follows:

Only a correspondence table between a possible second-type auxiliary bitposition number in a maximum mother code length and a transition pointindex number needs to be stored in the system, and then the positionnumbers of the J′ second-type auxiliary bits are selected according to apreset rule. For example, a transition point index number tcorresponding to K′ is first obtained through real-time calculation ortable lookup by using one of the foregoing methods. Then, a sequencecorresponding to the index number t in prestored position numbersequences of a mother code length N_(max) that are corresponding todifferent row weights is divided by N_(max)/N, an integer quotient isreserved, and J′ position numbers that are not of punctured subchannelsare sequentially selected from the reserved integer quotient in aleft-to-right order. Subchannels corresponding to the J′ positionnumbers are used to transmit the J′ second-type auxiliary bits. Itshould be noted that a position number meeting this rule is a reverseorder of a subchannel number. Therefore, after a position number X isobtained, a subchannel number of a second-type auxiliary bit needs to beobtained based on N−X.

For example, Table 9 shows a correspondence, in the case of N_(max)=512,between an index number and possible second-type auxiliary bit positionnumbers ranked in descending order of subchannel numbers. K′=242 andN=256 are still used as an example, and the index number t=1 may beobtained by searching Table 3. A position number sequence correspondingto t=1 in Table 9 is [256, 384, 448, 480, 496, 504, 508, 510, 511], andeach element in this sequence is divided by N_(max)/N=512/256=2, so that[128, 192, 224, 240, 248, 252, 254, 255, 255.5] can be obtained. Anon-integer quotient is removed and an integer quotient is reserved. Inthis case, obtained corresponding position numbers are [128, 192, 224,240, 248, 252, 254, 255], and a corresponding subchannel number sequenceis [128, 64, 32, 16, 8, 4, 2, 1]. It can be learned that this result iscompletely consistent with Method 5, Method 6, and Table 1.

Similarly, Table 10 shows a correspondence, in the case of N_(max)=512,between an index number and possible second-type auxiliary bit positionnumbers ranked in descending order of reliability. Table 11 shows acorrespondence, in the case of N_(max)=1024, between an index number andpossible second-type auxiliary bit position numbers ranked in descendingorder of subchannel numbers. Table 12 shows a correspondence, in thecase of N_(max)=1024, between an index number and possible second-typeauxiliary bit position numbers ranked in descending order ofreliability. These tables are also applicable to Method 5 and Method 6.

It should be noted that the “value range of K′” shown in Table 5 toTable 12 is only applicable to N_(max). A relationship between anothermother code length and K′, W_(min), or a transition point index numberis subject to Table 3 or Table 4.

Actually, it can also be learned that a value of a transition pointindex number in Table 3 and Table 4 is exactly equal to a minimumHamming distance corresponding to the K′ subchannels. This is becausethe table is made in a manner of determining K′ in ascending order ofW_(min), ensuring that K′ in a same column corresponds to same W_(min),and t=log₂ W_(min) is exactly met.

In addition, different mother code lengths shown in Table 1 to Table 12are merely examples, and other mother code lengths or other rankingmanners may also be made into such a table in a similar manner. Inactual application, only some content in the table may be used.

FIG. 4 is a schematic diagram of a polar code encoding apparatus 40according to this application. The apparatus 40 includes an encodingmodule 41, a determining module 42, and a sending module 43.

The encoding module 41 is configured to perform polar encoding on ato-be-encoded sequence, where a mother code length of a polar code is N,a sequence length obtained after encoding is M, and the to-be-encodedsequence includes frozen bits, first-type auxiliary bits, second-typeauxiliary bits, punctured bits, and information bits.

The determining module 42 is configured to determine subchannelscorresponding to the frozen bits, the first-type auxiliary bits, thesecond-type auxiliary bits, the punctured bits, and the informationbits. A method for selecting the second-type auxiliary bits includes butis not limited to the seven methods described in step 213 and step 214in the foregoing embodiment. The determining module 42 is furtherconfigured to determine values of the first-type auxiliary bits and thesecond-type auxiliary bits.

The sending module 43 is configured to send an encoded sequence.

A mother code length used in an encoding process is N, a code rate is R,a code length obtained after encoding is M, a quantity of informationbits is K, a quantity of first-type auxiliary bits is J, a quantity ofsecond-type auxiliary bits is J′, and K+J+J′=K′.

When N=M, there is no punctured bit, and an operation of determiningsubchannels of the punctured bits does not need to be performed.

When the quantity J′ of second-type auxiliary bits is not preset, thedetermining module 43 is further configured to calculate a value of J′.A specific method includes but is not limited to the method in step 213in the foregoing embodiment.

It should be noted that a rate matching module and the like are notshown in the figure, and details are not described because a specificrate matching manner is not related to this application.

FIG. 5 is a block diagram of a polar code decoding apparatus 50according to this application. The apparatus 50 includes an obtainingmodule 51, a determining module 52, and a decoding module 53.

The obtaining module 51 is configured to obtain a to-be-decodedsequence.

The determining module 52 is configured to determine subchannelscorresponding to frozen bits, first-type auxiliary bits, second-typeauxiliary bits, punctured bits, and information bits. A method forselecting the second-type auxiliary bits includes but is not limited tothe seven methods described in step 313 and step 314 in the foregoingembodiment.

The decoding module 53 is configured to perform polar decoding on thereceived to-be-decoded sequence to obtain a decoded sequence, where amother code length of a polar code is N.

A mother code length used in a decoding process is N, a code rate is R,a code length obtained after encoding is M, a quantity of informationbits is K, a quantity of first-type auxiliary bits is J, a quantity ofsecond-type auxiliary bits is J′, and K+J+J′=K′.

When the quantity J′ of second-type auxiliary bits is not preset, thedetermining module 52 is further configured to calculate a value of J′.A specific method includes but is not limited to the method in step 313in the foregoing embodiment.

FIG. 6 is a simplified block diagram of an encoding entity apparatus1100 according to this application. The apparatus 1100 includes a memory1101 and a processor 1102.

The memory 1101 is configured to store an execution instruction. Thememory may be a flash (flash memory).

The processor 1102 is configured to execute the execution instructionstored in the memory, to implement steps of the encoding method shown inFIG. 2. For details, refer to related descriptions in the foregoingmethod embodiment.

Optionally, the memory 1101 may be independent or may be integrated withthe processor 1102.

When the processor 1102 is implemented by hardware, for example, a logiccircuit or an integrated circuit, the processor 1102 is connected toother hardware by using an interface, and the memory may not be requiredin this case.

When the memory 1101 is a component independent of the processor 1102,the apparatus 1100 may further include a bus 1103, configured to connectthe memory and the processor.

The encoding apparatus in FIG. 6 may further include a transmitter (notshown in the figure), configured to send a sequence encoded by theprocessor 1102 through polar encoding.

In the foregoing sending device, there is at least one processor, andthe at least one processor is configured to execute acomputer-executable instruction stored in the memory, so that thesending device exchanges data with a receiving device by using acommunications interface, to perform the sending method provided in theforegoing various implementations.

FIG. 7 is a simplified block diagram of a decoding entity apparatus 1200according to this application. The apparatus 1200 includes a memory 1201and a processor 1202.

The memory 1201 is configured to store an execution instruction. Thememory may be a flash (flash memory).

The processor 1202 is configured to execute the execution instructionstored in the memory, to implement steps of the decoding method shown inFIG. 3. For details, refer to related descriptions in the foregoingmethod embodiment.

Optionally, the memory 1201 may be independent or may be integrated withthe processor 1202.

When the processor 1202 is implemented by hardware, for example, a logiccircuit or an integrated circuit, the processor 1202 is connected toother hardware by using an interface, and the memory may not be requiredin this case.

The decoding apparatus in FIG. 7 may further include a receiver (notshown in the figure), configured to: receive a to-be-decoded signal, andsend the to-be-decoded signal to the processor 1202.

In the foregoing receiving device, there is at least one processor, andthe at least one processor is configured to execute acomputer-executable instruction stored in the memory, so that thereceiving device exchanges data with a sending device by using acommunications interface, to perform the receiving method provided inthe foregoing various implementations.

This application further provides a computer readable storage medium.The computer readable storage medium stores a computer-executableinstruction, and when at least one processor of a sending deviceexecutes the computer-executable instruction, the sending deviceexecutes the data encoding method provided in the foregoing variousimplementations.

This application further provides a computer readable storage medium.The computer readable storage medium stores a computer-executableinstruction, and when at least one processor of a receiving deviceexecutes the computer-executable instruction, the receiving deviceexecutes the data decoding method provided in the foregoing variousimplementations.

This application further provides a computer program product. Thecomputer program product includes a computer-executable instruction, andthe computer-executable instruction is stored in a computer readablestorage medium. At least one processor of a sending device may read thecomputer-executable instruction from the computer readable storagemedium, and the at least one processor executes the computer-executableinstruction, so that the sending device implements the data encodingmethod provided in the foregoing various implementations.

This application further provides a computer program product. Thecomputer program product includes a computer-executable instruction, andthe computer-executable instruction is stored in a computer readablestorage medium. At least one processor of a receiving device may readthe computer-executable instruction from the computer readable storagemedium, and the at least one processor executes the computer-executableinstruction, so that the receiving device implements the data decodingmethod provided in the foregoing various implementations.

In the embodiment of the sending device or the receiving device, itshould be understood that the processor may be a central processing unit(CPU), or may be another general purpose processor, a digital signalprocessor (DSP), an application-specific integrated circuit (ASIC), orthe like. The general purpose processor may be a microprocessor or theprocessor may be any normal processor, or the like. The steps of themethod disclosed with reference to this application may be directlyperformed by a hardware processor, or may be performed by using acombination of hardware in the processor and a software module.

All or some steps of the foregoing method embodiment may be implementedby using a program instructing relevant hardware. The program may bestored in a computer readable memory. When the program is executed, thesteps of the foregoing method embodiment are performed. The foregoingmemory (storage medium) includes: a read-only memory (ROM), a randomaccess memory (RAM), a flash memory, a hard disk, a solid-state drive, amagnetic tape, a floppy disk, an optical disc, and any combinationthereof.

Finally, it should be noted that, although the solutions are describedin detail with reference to the foregoing embodiments, modifications tothe technical solutions described in the foregoing embodiments orequivalent replacements may still be made to some or all technicalfeatures thereof, without departing from the scope of the technicalsolutions of the embodiments of this application.

The tables described in the foregoing embodiments are as follows:

Table 1: Correspondence table of N, K′, and possible second-typeauxiliary bit subchannel numbers ranked in descending order ofsubchannel numbers

Table 2: Correspondence table of N, K′, and possible second-typeauxiliary bit subchannel numbers ranked in descending order ofsubchannel reliability

Table 3: Row weight transition point distribution in different mothercode lengths

Table 4: Row weight transition point distribution and W_(min)distribution in different mother code lengths

Table 5: Correspondence, in the case of N_(max)=512, between W_(min) andpossible second-type auxiliary bit position numbers ranked in descendingorder of subchannel numbers

Table 6: Correspondence, in the case of N_(max)=512, between W_(min) andpossible second-type auxiliary bit position numbers ranked in descendingorder of reliability

Table 7: Correspondence, in the case of N_(max)=1024, between W_(min)and possible second-type auxiliary bit position numbers ranked indescending order of subchannel numbers

Table 8: Correspondence, in the case of N_(max)=1024, between W_(min)and possible second-type auxiliary bit position numbers ranked indescending order of reliability

Table 9: Correspondence, in the case of N_(max)=512, between an indexand possible second-type auxiliary bit position numbers ranked indescending order of subchannel numbers

Table 10: Correspondence, in the case of N_(max)=512, between an indexand possible second-type auxiliary bit position numbers ranked indescending order of reliability

Table 11: Correspondence, in the case of N_(max)=1024, between an indexand possible second-type auxiliary bit position numbers ranked indescending order of subchannel numbers

Table 12: Correspondence, in the case of N_(max)=1024, between an indexand possible second-type auxiliary bit position numbers ranked indescending order of reliability

The tables are successively as follows:

TABLE 1 Correspondence table of N, K′, and possible second-typeauxiliary bit subchannel numbers ranked in descending order ofsubchannel numbers Value range of K′ Possible second-type auxiliary bitsubchannel numbers N = 4 2 ≤ K′ < 4 2, 1 N = 8 5 ≤ K′ < 8 4, 2, 1 2 ≤ K′< 5 6, 5, 3 N = 16 12 ≤ K′ < 16 8, 4, 2, 1  6 ≤ K′ < 12 12, 10, 9, 6, 5,3 2 ≤ K′ < 6 14, 13, 11, 7 N = 32 27 ≤ K′ < 32 16, 8, 4, 2, 1 16 ≤ K′ <27 24, 20, 18, 17, 12, 10, 9, 6, 5, 3  7 ≤ K′ < 16 28, 26, 25, 22, 21,19, 14, 13, 11, 7 2 ≤ K′ < 7 30, 29, 27, 23, 15 N = 64 57 ≤ K′ < 64 32,16, 8, 4, 2, 1 38 ≤ K′ < 57 48, 40, 36, 34, 33, 24, 20, 18, 17, 12, 10,9, 6, 5, 3 19 ≤ K′ < 38 56, 52, 50, 49, 44, 42, 41, 38, 37, 35, 28, 26,25, 22, 21, 19, 14, 13, 11, 7  7 ≤ K′ < 19 60, 58, 57, 54, 53, 51, 46,45, 43, 39, 30, 29, 27, 23, 15 2 ≤ K′ < 7 62, 61, 59, 55, 47, 31 N = 128117 ≤ K′ < 128 64, 32, 16, 8, 4, 2, 1  85 ≤ K′ < 117 96, 80, 72, 68, 66,65, 48, 40, 36, 34, 33, 24, 20, 18, 17, 12, 10, 9, 6, 5, 3 47 ≤ K′ < 85112, 104, 100, 98, 97, 88, 84, 82, 81, 76, 74, 73, 70, 69, 67, 56, 52,50, 49, 44, 42, 41, 38, 37, 35, 28, 26, 25, 22, 21, 19, 14, 13, 11, 7 20≤ K′ < 47 120, 116, 114, 113, 108, 106, 105, 102, 101, 99, 92, 90, 89,86, 85, 83, 78, 77, 75, 71, 60, 58, 57, 54, 53, 51, 46, 45, 43, 39, 30,29, 27, 23, 15  7 ≤ K′ < 20 124, 122, 121, 118, 117, 115, 110, 109, 107,103, 94, 93, 91, 87, 79, 62, 61, 59, 55, 47, 31 2 ≤ K′ < 7 126, 125,123, 119, 111, 95, 63 N = 256 240 ≤ K′ < 256 128, 64, 32, 16, 8, 4, 2, 1183 ≤ K′ < 240 192, 160, 144, 136, 132, 130, 129, 96, 80, 72, 68, 66,65, 48, 40, 36, 34, 33, 24, 20, 18, 17, 12, 10, 9, 6, 5, 3 109 ≤ K′ <183 224, 208, 200, 196, 194, 193, 176, 168, 164, 162, 161, 152, 148,146, 145, 140, 138, 137, 134, 133, 131, 112, 104, 100, 98, 97, 88, 84,82, 81, 76, 74, 73, 70, 69, 67, 56, 52, 50, 49, 44, 42, 41, 38, 37, 35,28, 26, 25, 22, 21, 19, 14, 13, 11, 7  52 ≤ K′ < 109 240, 232, 228, 226,225, 216, 212, 210, 209, 204, 202, 201, 198, 197, 195, 184, 180, 178,177, 172, 170, 169, 166, 165, 163, 156, 154, 153, 150, 149, 147, 142,141, 139, 135, 120, 116, 114, 113, 108, 106, 105, 102, 101, 99, 92, 90,89, 86, 85, 83, 78, 77, 75, 71, 60, 58, 57, 54, 53, 51, 46, 45, 43, 39,30, 29, 27, 23, 15 21 ≤ K′ < 52 248, 244, 242, 241, 236, 234, 233, 230,229, 227, 220, 218, 217, 214, 213, 211, 206, 205, 203, 199, 188, 186,185, 182, 181, 179, 174, 173, 171, 167, 158, 157, 155, 151, 143, 124,122, 121, 118, 117, 115, 110, 109, 107, 103, 94, 93, 91, 87, 79, 62, 61,59, 55, 47, 31  7 ≤ K′ < 21 252, 250, 249, 246, 245, 243, 238, 237, 235,231, 222, 221, 219, 215, 207, 190, 189, 187, 183, 175, 159, 126, 125,123, 119, 111, 95, 63 2 ≤ K′ < 7 254, 253, 251, 247, 239, 223, 191, 127N = 512 487 ≤ K′ < 512 256, 128, 64, 32, 16, 8, 4, 2, 1 387 ≤ K′ < 487384, 320, 288, 272, 264, 260, 258, 257, 192, 160, 144, 136, 132, 130,129, 96, 80, 72, 68, 66, 65, 48, 40, 36, 34, 33, 24, 20, 18, 17, 12, 10,9, 6, 5, 3 243 ≤ K′ < 387 448, 416, 400, 392, 388, 386, 385, 352, 336,328, 324, 322, 321, 304, 296, 292, 290, 289, 280, 276, 274, 273, 268,266, 265, 262, 261, 259, 224, 208, 200, 196, 194, 193, 176, 168, 164,162, 161, 152, 148, 146, 145, 140, 138, 137, 134, 133, 131, 112, 104,100, 98, 97, 88, 84, 82, 81, 76, 74, 73, 70, 69, 67, 56, 52, 50, 49, 44,42, 41, 38, 37, 35, 28, 26, 25, 22, 21, 19, 14, 13, 11, 7 125 ≤ K′ < 243480, 464, 456, 452, 450, 449, 432, 424, 420, 418, 417, 408, 404, 402,401, 396, 394, 393, 390, 389, 387, 368, 360, 356, 354, 353, 344, 340,338, 337, 332, 330, 329, 326, 325, 323, 312, 308, 306, 305, 300, 298,297, 294, 293, 291, 284, 282, 281, 278, 277, 275, 270, 269, 267, 263,240, 232, 228, 226, 225, 216, 212, 210, 209, 204, 202, 201, 198, 197,195, 184, 180, 178, 177, 172, 170, 169, 166, 165, 163, 156, 154, 153,150, 149, 147, 142, 141, 139, 135, 120, 116, 114, 113, 108, 106, 105,102, 101, 99, 92, 90, 89, 86, 85, 83, 78, 77, 75, 71, 60, 58, 57, 54,53, 51, 46, 45, 43, 39, 30, 29, 27, 23, 15  55 ≤ K′ < 125 496, 488, 484,482, 481, 472, 468, 466, 465, 460, 458, 457, 454, 453, 451, 440, 436,434, 433, 428, 426, 425, 422, 421, 419, 412, 410, 409, 406, 405, 403,398, 397, 395, 391, 376, 372, 370, 369, 364, 362, 361, 358, 357, 355,348, 346, 345, 342, 341, 339, 334, 333, 331, 327, 316, 314, 313, 310,309, 307, 302, 301, 299, 295, 286, 285, 283, 279, 271, 248, 244, 242,241, 236, 234, 233, 230, 229, 227, 220, 218, 217, 214, 213, 211, 206,205, 203, 199, 188, 186, 185, 182, 181, 179, 174, 173, 171, 167, 158,157, 155, 151, 143, 124, 122, 121, 118, 117, 115, 110, 109, 107, 103,94, 93, 91, 87, 79, 62, 61, 59, 55, 47, 31 21 ≤ K′ < 55 504, 500, 498,497, 492, 490, 489, 486, 485, 483, 476, 474, 473, 470, 469, 467, 462,461, 459, 455, 444, 442, 441, 438, 437, 435, 430, 429, 427, 423, 414,413, 411, 407, 399, 380, 378, 377, 374, 373, 371, 366, 365, 363, 359,350, 349, 347, 343, 335, 318, 317, 315, 311, 303, 287, 252, 250, 249,246, 245, 243, 238, 237, 235, 231, 222, 221, 219, 215, 207, 190, 189,187, 183, 175, 159, 126, 125, 123, 119, 111, 95, 63  7 ≤ K′ < 21 508,506, 505, 502, 501, 499, 494, 493, 491, 487, 478, 477, 475, 471, 463,446, 445, 443, 439, 431, 415, 382, 381, 379, 375, 367, 351, 319, 254,253, 251, 247, 239, 223, 191, 127 2 ≤ K′ < 7 510, 509, 507, 503, 495,479, 447, 383, 255 N = 1024  984 ≤ K′ < 1024 512, 256, 128, 64, 32, 16,8, 4, 2, 1 805 ≤ K′ < 984 768, 640, 576, 544, 528, 520, 516, 514, 513,384, 320, 288, 272, 264, 260, 258, 257, 192, 160, 144, 136, 132, 130,129, 96, 80, 72, 68, 66, 65, 48, 40, 36, 34, 33, 24, 20, 18, 17, 12, 10,9, 6, 5, 3 531 ≤ K′ < 805 896, 832, 800, 784, 776, 772, 770, 769, 704,672, 656, 648, 644, 642, 641, 608, 592, 584, 580, 578, 577, 560, 552,548, 546, 545, 536, 532, 530, 529, 524, 522, 521, 518, 517, 515, 448,416, 400, 392, 388, 386, 385, 352, 336, 328, 324, 322, 321, 304, 296,292, 290, 289, 280, 276, 274, 273, 268, 266, 265, 262, 261, 259, 224,208, 200, 196, 194, 193, 176, 168, 164, 162, 161, 152, 148, 146, 145,140, 138, 137, 134, 133, 131, 112, 104, 100, 98, 97, 88, 84, 82, 81, 76,74, 73, 70, 69, 67, 56, 52, 50, 49, 44, 42, 41, 38, 37, 35, 28, 26, 25,22, 21, 19, 14, 13, 11, 7 287 ≤ K′ < 531 960, 928, 912, 904, 900, 898,897, 864, 848, 840, 836, 834, 833, 816, 808, 804, 802, 801, 792, 788,786, 785, 780, 778, 777, 774, 773, 771, 736, 720, 712, 708, 706, 705,688, 680, 676, 674, 673, 664, 660, 658, 657, 652, 650, 649, 646, 645,643, 624, 616, 612, 610, 609, 600, 596, 594, 593, 588, 586, 585, 582,581, 579, 568, 564, 562, 561, 556, 554, 553, 550, 549, 547, 540, 538,537, 534, 533, 531, 526, 525, 523, 519, 480, 464, 456, 452, 450, 449,432, 424, 420, 418, 417, 408, 404, 402, 401, 396, 394, 393, 390, 389,387, 368, 360, 356, 354, 353, 344, 340, 338, 337, 332, 330, 329, 326,325, 323, 312, 308, 306, 305, 300, 298, 297, 294, 293, 291, 284, 282,281, 278, 277, 275, 270, 269, 267, 263, 240, 232, 228, 226, 225, 216,212, 210, 209, 204, 202, 201, 198, 197, 195, 184, 180, 178, 177, 172,170, 169, 166, 165, 163, 156, 154, 153, 150, 149, 147, 142, 141, 139,135, 120, 116, 114, 113, 108, 106, 105, 102, 101, 99, 92, 90, 89, 86,85, 83, 78, 77, 75, 71, 60, 58, 57, 54, 53, 51, 46, 45, 43, 39, 30, 29,27, 23, 15 134 ≤ K′ < 287 992, 976, 968, 964, 962, 961, 944, 936, 932,930, 929, 920, 916, 914, 913, 908, 906, 905, 902, 901, 899, 880, 872,868, 866, 865, 856, 852, 850, 849, 844, 842, 841, 838, 837, 835, 824,820, 818, 817, 812, 810, 809, 806, 805, 803, 796, 794, 793, 790, 789,787, 782, 781, 779, 775, 752, 744, 740, 738, 737, 728, 724, 722, 721,716, 714, 713, 710, 709, 707, 696, 692, 690, 689, 684, 682, 681, 678,677, 675, 668, 666, 665, 662, 661, 659, 654, 653, 651, 647, 632, 628,626, 625, 620, 618, 617, 614, 613, 611, 604, 602, 601, 598, 597, 595,590, 589, 587, 583, 572, 570, 569, 566, 565, 563, 558, 557, 555, 551,542, 541, 539, 535, 527, 496, 488, 484, 482, 481, 472, 468, 466, 465,460, 458, 457, 454, 453, 451, 440, 436, 434, 433, 428, 426, 425, 422,421, 419, 412, 410, 409, 406, 405, 403, 398, 397, 395, 391, 376, 372,370, 369, 364, 362, 361, 358, 357, 355, 348, 346, 345, 342, 341, 339,334, 333, 331, 327, 316, 314, 313, 310, 309, 307, 302, 301, 299, 295,286, 285, 283, 279, 271, 248, 244, 242, 241, 236, 234, 233, 230, 229,227, 220, 218, 217, 214, 213, 211, 206, 205, 203, 199, 188, 186, 185,182, 181, 179, 174, 173, 171, 167, 158, 157, 155, 151, 143, 124, 122,121, 118, 117, 115, 110, 109, 107, 103, 94, 93, 91, 87, 79, 62, 61, 59,55, 47, 31  56 ≤ K′ < 134 1008, 1000, 996, 994, 993, 984, 980, 978, 977,972, 970, 969, 966, 965, 963, 952, 948, 946, 945, 940, 938, 937, 934,933, 931, 924, 922, 921, 918, 917, 915, 910, 909, 907, 903, 888, 884,882, 881, 876, 874, 873, 870, 869, 867, 860, 858, 857, 854, 853, 851,846, 845, 843, 839, 828, 826, 825, 822, 821, 819, 814, 813, 811, 807,798, 797, 795, 791, 783, 760, 756, 754, 753, 748, 746, 745, 742, 741,739, 732, 730, 729, 726, 725, 723, 718, 717, 715, 711, 700, 698, 697,694, 693, 691, 686, 685, 683, 679, 670, 669, 667, 663, 655, 636, 634,633, 630, 629, 627, 622, 621, 619, 615, 606, 605, 603, 599, 591, 574,573, 571, 567, 559, 543, 504, 500, 498, 497, 492, 490, 489, 486, 485,483, 476, 474, 473, 470, 469, 467, 462, 461, 459, 455, 444, 442, 441,438, 437, 435, 430, 429, 427, 423, 414, 413, 411, 407, 399, 380, 378,377, 374, 373, 371, 366, 365, 363, 359, 350, 349, 347, 343, 335, 318,317, 315, 311, 303, 287, 252, 250, 249, 246, 245, 243, 238, 237, 235,231, 222, 221, 219, 215, 207, 190, 189, 187, 183, 175, 159, 126, 125,123, 119, 111, 95, 63 21 ≤ K′ < 56 1016, 1012, 1010, 1009, 1004, 1002,1001, 998, 997, 995, 988, 986, 985, 982, 981, 979, 974, 973, 971, 967,956, 954, 953, 950, 949, 947, 942, 941, 939, 935, 926, 925, 923, 919,911, 892, 890, 889, 886, 885, 883, 878, 877, 875, 871, 862, 861, 859,855, 847, 830, 829, 827, 823, 815, 799, 764, 762, 761, 758, 757, 755,750, 749, 747, 743, 734, 733, 731, 727, 719, 702, 701, 699, 695, 687,671, 638, 637, 635, 631, 623, 607, 575, 508, 506, 505, 502, 501, 499,494, 493, 491, 487, 478, 477, 475, 471, 463, 446, 445, 443, 439, 431,415, 382, 381, 379, 375, 367, 351, 319, 254, 253, 251, 247, 239, 223,191, 127  7 ≤ K′ < 21 1020, 1018, 1017, 1014, 1013, 1011, 1006, 1005,1003, 999, 990, 989, 987, 983, 975, 958, 957, 955, 951, 943, 927, 894,893, 891, 887, 879, 863, 831, 766, 765, 763, 759, 751, 735, 703, 639,510, 509, 507, 503, 495, 479, 447, 383, 255 2 ≤ K′ < 7 1022, 1021, 1019,1015, 1007, 991, 959, 895, 767, 511

TABLE 2 Correspondence table of N, K′, and possible second-typeauxiliary bit subchannel numbers ranked in descending order ofsubchannel reliability Value range of K′ Possible second-type auxiliarybit subchannel numbers N = 4 2 ≤ K′ < 4 2, 1 N = 8 5 ≤ K′ < 8 4, 2, 1 2≤ K′ < 5 6, 5, 3 N = 16 12 ≤ K′ < 16 8, 4, 2, 1 6 ≤ K′ < 12 12, 10, 9,6, 5, 3 2 ≤ K′ < 6 14, 13, 11, 7 N = 32 27 ≤ K′ < 32 16, 8, 4, 2, 1 16 ≤K′ < 27 24, 20, 18, 12, 17, 10, 9, 6, 5, 3 7 ≤ K′ < 16 28, 26, 25, 22,21, 14, 19, 13, 11, 7 2 ≤ K′ < 7 30, 29, 27, 23, 15 N = 64 57 ≤ K′ < 6432, 16, 8, 4, 2, 1 38 ≤ K′ < 57 48, 40, 36, 24, 34, 20, 33, 18, 12, 17,10, 9, 6, 5, 3 19 ≤ K′ < 38 56, 52, 50, 44, 49, 42, 28, 41, 38, 26, 37,25, 22, 35, 21, 14, 19, 13, 11, 7 7 ≤ K′ < 19 60, 58, 57, 54, 53, 46,51, 45, 30, 43, 29, 39, 27, 23, 15 2 ≤ K′ < 7 62, 61, 59, 55, 47, 31 N =128 117 ≤ K′ < 128 64, 32, 16, 8, 4, 2, 1 85 ≤ K′ < 117 96, 80, 72, 48,68, 40, 66, 65, 36, 24, 34, 20, 33, 18, 12, 17, 10, 9, 6, 5, 3 47 ≤ K′ <85 112, 104, 100, 88, 98, 84, 97, 56, 82, 76, 81, 52, 74, 50, 73, 44,70, 49, 42, 69, 28, 41, 67, 38, 26, 37, 25, 22, 35, 21, 14, 19, 13, 11,7 20 ≤ K′ < 47 120, 116, 114, 108, 113, 106, 92, 105, 102, 90, 101, 89,60, 86, 99, 58, 85, 78, 57, 83, 54, 77, 53, 75, 46, 51, 45, 71, 30, 43,29, 39, 27, 23, 15 7 ≤ K′ < 20 124, 122, 121, 118, 117, 110, 115, 109,94, 107, 93, 103, 91, 62, 61, 87, 59, 79, 55, 47, 31 2 ≤ K′ < 7 126,125, 123, 119, 111, 95, 63 N = 256 240 ≤ K′ < 256 128, 64, 32, 16, 8, 4,2, 1 183 ≤ K′ < 240 192, 160, 144, 96, 136, 80, 132, 130, 72, 48, 129,68, 40, 66, 65, 36, 24, 34, 20, 33, 18, 12, 17, 10, 9, 6, 5, 3 109 ≤ K′< 183 224, 208, 200, 176, 196, 168, 194, 112, 193, 164, 152, 162, 104,148, 161, 100, 146, 88, 140, 98, 145, 84, 138, 97, 56, 137, 82, 134, 76,81, 52, 133, 74, 50, 131, 73, 44, 70, 49, 42, 69, 28, 41, 67, 38, 26,37, 25, 22, 35, 21, 14, 19, 13, 11, 7 52 ≤ K′ < 109 240, 232, 228, 216,226, 212, 225, 184, 210, 204, 209, 180, 202, 178, 120, 201, 172, 198,177, 116, 170, 197, 156, 169, 114, 195, 166, 108, 154, 113, 165, 106,153, 150, 163, 92, 105, 102, 149, 90, 142, 101, 147, 89, 60, 141, 86,99, 58, 85, 139, 78, 57, 83, 54, 135, 77, 53, 75, 46, 51, 45, 71, 30,43, 29, 39, 27, 23, 15 21 ≤ K′ < 52 248, 244, 242, 236, 241, 234, 220,233, 230, 218, 229, 217, 188, 214, 227, 186, 213, 206, 185, 211, 182,124, 205, 181, 122, 203, 174, 179, 121, 173, 118, 199, 158, 117, 171,110, 157, 115, 167, 109, 155, 94, 107, 151, 93, 103, 91, 62, 143, 61,87, 59, 79, 55, 47, 31 7 ≤ K′ < 21 252, 250, 249, 246, 245, 238, 243,237, 222, 235, 221, 231, 219, 190, 189, 215, 187, 126, 207, 183, 125,123, 175, 119, 159, 111, 95, 63 2 ≤ K′ < 7 254, 253, 251, 247, 239, 223,191, 127 N = 512 487 ≤ K′ < 512 256, 128, 64, 32, 16, 8, 4, 2, 1 387 ≤K′ < 487 384, 320, 288, 192, 272, 160, 264, 260, 144, 96, 258, 136, 257,80, 132, 130, 72, 48, 129, 68, 40, 66, 65, 36, 24, 34, 20, 33, 18, 12,17, 10, 9, 6, 5, 3 243 ≤ K′ < 387 448, 416, 400, 352, 392, 336, 388,224, 386, 328, 304, 385, 324, 208, 296, 322, 200, 321, 292, 176, 280,196, 290, 168, 276, 194, 289, 112, 193, 274, 164, 268, 152, 273, 162,104, 266, 148, 161, 265, 100, 262, 146, 88, 140, 261, 98, 145, 84, 138,97, 259, 56, 137, 82, 134, 76, 81, 52, 133, 74, 50, 131, 73, 44, 70, 49,42, 69, 28, 41, 67, 38, 26, 37, 25, 22, 35, 21, 14, 19, 13, 11, 7 125 ≤K′ < 243 480, 464, 456, 432, 452, 424, 450, 368, 449, 420, 408, 418,360, 404, 417, 356, 240, 402, 344, 396, 354, 401, 232, 340, 394, 353,312, 393, 338, 228, 390, 332, 216, 337, 308, 389, 226, 330, 212, 225,306, 387, 329, 300, 326, 184, 210, 305, 204, 298, 325, 209, 180, 284,202, 297, 323, 294, 178, 120, 201, 282, 172, 198, 293, 177, 281, 116,170, 197, 278, 291, 156, 169, 277, 114, 195, 166, 108, 270, 154, 113,275, 165, 269, 106, 153, 150, 163, 92, 105, 267, 102, 149, 90, 142, 101,263, 147, 89, 60, 141, 86, 99, 58, 85, 139, 78, 57, 83, 54, 135, 77, 53,75, 46, 51, 45, 71, 30, 43, 29, 39, 27, 23, 15 55 ≤ K′ < 125 496, 488,484, 472, 482, 468, 481, 440, 466, 460, 465, 436, 458, 434, 376, 457,428, 454, 433, 372, 426, 453, 412, 425, 370, 451, 422, 364, 248, 410,369, 421, 362, 409, 244, 406, 419, 348, 361, 358, 405, 242, 346, 236,398, 357, 241, 403, 345, 316, 397, 234, 342, 355, 220, 233, 314, 341,395, 230, 334, 218, 313, 339, 229, 310, 391, 333, 217, 188, 214, 309,227, 331, 302, 186, 213, 307, 206, 301, 327, 185, 211, 182, 124, 205,286, 299, 181, 285, 122, 203, 174, 295, 179, 121, 283, 173, 118, 199,158, 117, 171, 279, 110, 157, 115, 167, 109, 271, 155, 94, 107, 151, 93,103, 91, 62, 143, 61, 87, 59, 79, 55, 47, 31 21 ≤ K′ < 55 504, 500, 498,492, 497, 490, 476, 489, 486, 474, 485, 473, 444, 470, 483, 442, 469,462, 441, 467, 438, 380, 461, 437, 378, 459, 430, 435, 377, 429, 374,455, 252, 414, 373, 427, 366, 413, 250, 371, 423, 365, 249, 411, 246,350, 363, 245, 407, 349, 238, 359, 243, 347, 237, 318, 399, 222, 317,235, 343, 221, 315, 231, 335, 219, 190, 311, 189, 215, 303, 187, 126,207, 183, 125, 287, 123, 175, 119, 159, 111, 95, 63 7 ≤ K′ < 21 508,506, 505, 502, 501, 494, 499, 493, 478, 491, 477, 487, 475, 446, 445,471, 443, 382, 463, 439, 381, 379, 431, 254, 375, 253, 415, 367, 251,247, 351, 239, 319, 223, 191, 127 2 ≤ K′ < 7 510, 509, 507, 503, 495,479, 447, 383, 255 N = 1024 984 ≤ K′ < 1024 512, 256, 128, 64, 32, 16,8, 4, 2, 1 805 ≤ K′ < 984 768, 640, 576, 384, 544, 320, 528, 520, 288,192, 516, 272, 514, 513, 160, 264, 260, 144, 96, 258, 136, 257, 80, 132,130, 72, 48, 129, 68, 40, 66, 65, 36, 24, 34, 20, 33, 18, 12, 17, 10, 9,6, 5, 3 531 ≤ K′ < 805 896, 832, 800, 704, 784, 672, 776, 448, 772, 656,608, 770, 648, 769, 416, 592, 644, 400, 642, 584, 352, 560, 641, 392,580, 336, 552, 388, 578, 577, 224, 386, 548, 328, 536, 304, 385, 546,324, 208, 532, 545, 296, 322, 530, 200, 524, 321, 292, 529, 176, 280,522, 196, 290, 521, 168, 276, 194, 289, 518, 112, 193, 274, 517, 164,268, 152, 273, 515, 162, 104, 266, 148, 161, 265, 100, 262, 146, 88,140, 261, 98, 145, 84, 138, 97, 259, 56, 137, 82, 134, 76, 81, 52, 133,74, 50, 131, 73, 44, 70, 49, 42, 69, 28, 41, 67, 38, 26, 37, 25, 22, 35,21, 14, 19, 13, 11, 7 287 ≤ K′ < 531 960, 928, 912, 864, 904, 848, 900,736, 898, 840, 816, 897, 836, 720, 808, 834, 712, 833, 480, 804, 688,792, 708, 802, 464, 680, 788, 706, 801, 624, 705, 786, 676, 456, 780,664, 785, 432, 674, 616, 778, 452, 660, 673, 777, 424, 450, 612, 774,658, 600, 652, 368, 449, 773, 420, 610, 657, 408, 596, 650, 609, 771,418, 360, 568, 649, 404, 594, 417, 646, 588, 356, 593, 240, 402, 564,645, 344, 396, 586, 354, 401, 562, 643, 585, 232, 340, 394, 556, 353,582, 561, 312, 393, 338, 554, 581, 228, 390, 332, 216, 540, 337, 553,308, 389, 579, 226, 550, 330, 538, 212, 225, 306, 387, 549, 329, 300,537, 326, 184, 210, 305, 534, 547, 204, 298, 325, 209, 533, 180, 284,202, 297, 526, 323, 294, 531, 178, 120, 201, 282, 525, 172, 198, 293,177, 281, 523, 116, 170, 197, 278, 291, 156, 169, 277, 114, 195, 519,166, 108, 270, 154, 113, 275, 165, 269, 106, 153, 150, 163, 92, 105,267, 102, 149, 90, 142, 101, 263, 147, 89, 60, 141, 86, 99, 58, 85, 139,78, 57, 83, 54, 135, 77, 53, 75, 46, 51, 45, 71, 30, 43, 29, 39, 27, 23,15 134 ≤ K′ < 287 992, 976, 968, 944, 964, 936, 962, 880, 961, 932, 920,930, 872, 916, 929, 868, 752, 914, 856, 908, 866, 913, 744, 852, 906,865, 824, 905, 850, 740, 902, 844, 728, 849, 496, 820, 901, 738, 842,724, 737, 818, 899, 841, 488, 812, 838, 696, 722, 817, 716, 810, 837,484, 721, 692, 472, 796, 714, 809, 835, 482, 806, 690, 632, 713, 794,468, 684, 481, 710, 805, 689, 793, 440, 466, 628, 682, 709, 790, 803,460, 668, 465, 681, 789, 436, 626, 707, 678, 458, 620, 782, 666, 625,787, 434, 677, 376, 457, 781, 428, 618, 665, 454, 433, 662, 675, 604,617, 779, 372, 426, 453, 614, 661, 412, 602, 425, 654, 370, 451, 613,775, 422, 659, 364, 601, 248, 410, 572, 653, 369, 598, 421, 611, 362,409, 570, 597, 651, 244, 406, 419, 348, 361, 590, 569, 358, 405, 595,242, 566, 647, 346, 589, 236, 398, 357, 241, 403, 565, 345, 316, 397,587, 234, 342, 558, 355, 563, 220, 233, 314, 341, 395, 557, 583, 230,334, 218, 313, 542, 339, 555, 229, 310, 391, 333, 217, 541, 188, 214,309, 227, 551, 331, 302, 539, 186, 213, 307, 206, 301, 327, 185, 211,535, 182, 124, 205, 286, 299, 181, 285, 122, 203, 527, 174, 295, 179,121, 283, 173, 118, 199, 158, 117, 171, 279, 110, 157, 115, 167, 109,271, 155, 94, 107, 151, 93, 103, 91, 62, 143, 61, 87, 59, 79, 55, 47, 3156 ≤ K′ < 134 1008, 1000, 996, 984, 994, 980, 993, 952, 978, 972, 977,948, 970, 946, 888, 969, 940, 966, 945, 884, 938, 965, 924, 937, 882,963, 934, 876, 760, 922, 881, 933, 874, 921, 756, 918, 931, 860, 873,870, 917, 754, 858, 748, 910, 869, 753, 915, 857, 504, 828, 909, 746,854, 867, 732, 745, 826, 853, 907, 500, 742, 846, 730, 825, 851, 498,741, 822, 903, 845, 492, 729, 700, 497, 726, 821, 739, 843, 490, 814,698, 725, 819, 476, 489, 718, 813, 839, 697, 486, 723, 694, 474, 636,717, 798, 811, 485, 693, 473, 797, 444, 634, 715, 470, 686, 483, 807,691, 633, 795, 442, 469, 685, 630, 711, 462, 441, 670, 467, 629, 683,791, 438, 380, 461, 622, 669, 437, 627, 679, 378, 459, 621, 783, 430,667, 435, 377, 606, 429, 619, 374, 455, 663, 605, 252, 414, 373, 427,615, 366, 413, 603, 250, 574, 655, 371, 423, 365, 249, 411, 573, 599,246, 350, 363, 571, 245, 407, 349, 591, 238, 359, 243, 567, 347, 237,318, 399, 222, 317, 235, 343, 559, 221, 315, 231, 335, 219, 543, 190,311, 189, 215, 303, 187, 126, 207, 183, 125, 287, 123, 175, 119, 159,111, 95, 63 21 ≤ K′ < 56 1016, 1012, 1010, 1004, 1009, 1002, 988, 1001,998, 986, 997, 985, 956, 982, 995, 954, 981, 974, 953, 979, 950, 892,973, 949, 890, 971, 942, 947, 889, 941, 886, 967, 764, 926, 885, 939,878, 925, 762, 883, 935, 877, 761, 923, 758, 862, 875, 757, 919, 861,508, 750, 871, 755, 859, 506, 749, 830, 911, 505, 734, 829, 747, 855,502, 733, 827, 501, 743, 847, 494, 731, 702, 499, 823, 493, 701, 727,478, 491, 815, 699, 477, 638, 719, 487, 695, 475, 637, 799, 446, 445,635, 471, 687, 443, 631, 382, 463, 671, 439, 381, 623, 379, 431, 607,254, 375, 253, 415, 367, 251, 575, 247, 351, 239, 319, 223, 191, 127 7 ≤K′ < 21 1020, 1018, 1017, 1014, 1013, 1006, 1011, 1005, 990, 1003, 989,999, 987, 958, 957, 983, 955, 894, 975, 951, 893, 891, 943, 766, 887,765, 927, 879, 763, 759, 863, 510, 509, 751, 507, 831, 735, 503, 495,703, 479, 639, 447, 383, 255 2 ≤ K′ < 7 1022, 1021, 1019, 1015, 1007,991, 959, 895, 767, 511

TABLE 3 Row weight transition point distribution in different mothercode lengths Index t 1 2 3 4 5 6 7 8 9 N = 4 2 N = 8 5 2 N = 16 12 6 2 N= 32 27 16 7 2 N = 64 57 38 19 7 2 N = 128 117 85 47 20 7 2 N = 256 240183 109 52 21 7 2 N = 512 487 387 243 125 55 21 7 2 N = 1024 984 805 531287 134 56 21 7 2Note: A number in rows in which different values of N are located in thetable represents a row weight transition point K_(t).

TABLE 4 Row weight transition point distribution and W_(min)distribution in different mother code lengths t 1 2 3 4 5 6 7 8 9W_(min) 2 4 8 16 32 64 128 256 512 N = 4 2 N = 8 5 2 N = 16 12 6 2 N =32 27 16 7 2 N = 64 57 38 19 7 2 N = 128 117 85 47 20 7 2 N = 256 240183 109 52 21 7 2 N = 512 487 387 243 125 55 21 7 2 N = 1024 984 805 531287 134 56 21 7 2Note: A number in rows in which different values of N are located in thetable represents a row weight transition point K_(t).

TABLE 5 Correspondence, in the case of N_(max) = 512, between W_(min)and possible second-type auxiliary bit position numbers ranked indescending order of subchannel numbers N_(max) = 512 Value range ofPossible second-type auxiliary bit subchannel position W_(min) K′numbers 2 487 ≤ K′ < 512 256, 384, 448, 480, 496, 504, 508, 510, 511 4387 ≤ K′ < 487 128, 192, 224, 240, 248, 252, 254, 255, 320, 352, 368,376, 380, 382, 383, 416, 432, 440, 444, 446, 447, 464, 472, 476, 478,479, 488, 492, 494, 495, 500, 502, 503, 506, 507, 509 8 243 ≤ K′ < 38764, 96, 112, 120, 124, 126, 127, 160, 176, 184, 188, 190, 191, 208, 216,220, 222, 223, 232, 236, 238, 239, 244, 246, 247, 250, 251, 253, 288,304, 312, 316, 318, 319, 336, 344, 348, 350, 351, 360, 364, 366, 367,372, 374, 375, 378, 379, 381, 400, 408, 412, 414, 415, 424, 428, 430,431, 436, 438, 439, 442, 443, 445, 456, 460, 462, 463, 468, 470, 471,474, 475, 477, 484, 486, 487, 490, 491, 493, 498, 499, 501, 505 16 125 ≤K′ < 243 32, 48, 56, 60, 62, 63, 80, 88, 92, 94, 95, 104, 108, 110, 111,116, 118, 119, 122, 123, 125, 144, 152, 156, 158, 159, 168, 172, 174,175, 180, 182, 183, 186, 187, 189, 200, 204, 206, 207, 212, 214, 215,218, 219, 221, 228, 230, 231, 234, 235, 237, 242, 243, 245, 249, 272,280, 284, 286, 287, 296, 300, 302, 303, 308, 310, 311, 314, 315, 317,328, 332, 334, 335, 340, 342, 343, 346, 347, 349, 356, 358, 359, 362,363, 365, 370, 371, 373, 377, 392, 396, 398, 399, 404, 406, 407, 410,411, 413, 420, 422, 423, 426, 427, 429, 434, 435, 437, 441, 452, 454,455, 458, 459, 461, 466, 467, 469, 473, 482, 483, 485, 489, 497 32 55 ≤K′ < 125 16, 24, 28, 30, 31, 40, 44, 46, 47, 52, 54, 55, 58, 59, 61, 72,76, 78, 79, 84, 86, 87, 90, 91, 93, 100, 102, 103, 106, 107, 109, 114,115, 117, 121, 136, 140, 142, 143, 148, 150, 151, 154, 155, 157, 164,166, 167, 170, 171, 173, 178, 179, 181, 185, 196, 198, 199, 202, 203,205, 210, 211, 213, 217, 226, 227, 229, 233, 241, 264, 268, 270, 271,276, 278, 279, 282, 283, 285, 292, 294, 295, 298, 299, 301, 306, 307,309, 313, 324, 326, 327, 330, 331, 333, 338, 339, 341, 345, 354, 355,357, 361, 369, 388, 390, 391, 394, 395, 397, 402, 403, 405, 409, 418,419, 421, 425, 433, 450, 451, 453, 457, 465, 481 64 21 ≤ K′ < 55 8, 12,14, 15, 20, 22, 23, 26, 27, 29, 36, 38, 39, 42, 43, 45, 50, 51, 53, 57,68, 70, 71, 74, 75, 77, 82, 83, 85, 89, 98, 99, 101, 105, 113, 132, 134,135, 138, 139, 141, 146, 147, 149, 153, 162, 163, 165, 169, 177, 194,195, 197, 201, 209, 225, 260, 262, 263, 266, 267, 269, 274, 275, 277,281, 290, 291, 293, 297, 305, 322, 323, 325, 329, 337, 353, 386, 387,389, 393, 401, 417, 449 128 7 ≤ K′ < 21 4, 6, 7, 10, 11, 13, 18, 19, 21,25, 34, 35, 37, 41, 49, 66, 67, 69, 73, 81, 97, 130, 131, 133, 137, 145,161, 193, 258, 259, 261, 265, 273, 289, 321, 385 256 2 ≤ K′ < 7 2, 3, 5,9, 17, 33, 65, 129, 257Note: A subchannel number of a selected second-type auxiliary bit isN−X_(j), where j=1, 2, . . . , or J′.

TABLE 6 Correspondence, in the case of N_(max) = 512, between W_(min)and possible second-type auxiliary bit position numbers ranked indescending order of reliability N_(max) = 512 Value range of Possiblesecond-type auxiliary bit subchannel position W_(min) K′ numbers 2 487 ≤K′ < 512 256, 384, 448, 480, 496, 504, 508, 510, 511 4 387 ≤ K′ < 487128, 192, 224, 320, 240, 352, 248, 252, 368, 416, 254, 376, 255, 432,380, 382, 440, 464, 383, 444, 472, 446, 447, 476, 488, 478, 492, 479,494, 500, 495, 502, 503, 506, 507, 509 8 243 ≤ K′ < 387 64, 96, 112,160, 120, 176, 124, 288, 126, 184, 208, 127, 188, 304, 216, 190, 312,191, 220, 336, 232, 316, 222, 344, 236, 318, 223, 400, 319, 238, 348,244, 360, 239, 350, 408, 246, 364, 351, 247, 412, 250, 366, 424, 372,251, 414, 367, 428, 374, 415, 253, 456, 375, 430, 378, 436, 431, 460,379, 438, 462, 381, 439, 468, 442, 463, 470, 443, 484, 471, 445, 474,486, 475, 487, 490, 477, 491, 498, 493, 499, 501, 505 16 125 ≤ K′ < 24332, 48, 56, 80, 60, 88, 62, 144, 63, 92, 104, 94, 152, 108, 95, 156,272, 110, 168, 116, 158, 111, 280, 172, 118, 159, 200, 119, 174, 284,122, 180, 296, 175, 204, 123, 286, 182, 300, 287, 206, 125, 183, 212,186, 328, 302, 207, 308, 214, 187, 303, 332, 228, 310, 215, 189, 218,334, 392, 311, 230, 340, 314, 219, 335, 231, 396, 342, 315, 234, 221,356, 343, 235, 398, 317, 346, 404, 242, 358, 399, 237, 347, 243, 406,359, 362, 349, 420, 407, 245, 410, 363, 422, 370, 411, 249, 365, 423,452, 371, 426, 413, 454, 427, 373, 434, 455, 429, 458, 377, 435, 459,437, 466, 461, 467, 441, 482, 469, 483, 473, 485, 489, 497 32 55 ≤ K′ <125 16, 24, 28, 40, 30, 44, 31, 72, 46, 52, 47, 76, 54, 78, 136, 55, 84,58, 79, 140, 86, 59, 100, 87, 142, 61, 90, 148, 264, 102, 143, 91, 150,103, 268, 106, 93, 164, 151, 154, 107, 270, 166, 276, 114, 155, 271,109, 167, 196, 115, 278, 170, 157, 292, 279, 198, 171, 117, 282, 178,294, 199, 173, 283, 202, 121, 179, 295, 324, 298, 203, 285, 181, 210,326, 299, 205, 306, 211, 185, 327, 301, 330, 388, 307, 226, 213, 331,227, 390, 309, 338, 217, 333, 391, 229, 339, 394, 313, 354, 395, 341,233, 402, 355, 397, 345, 403, 241, 357, 418, 405, 361, 419, 409, 421,450, 369, 451, 425, 453, 433, 457, 465, 481 64 21 ≤ K′ < 55 8, 12, 14,20, 15, 22, 36, 23, 26, 38, 27, 39, 68, 42, 29, 70, 43, 50, 71, 45, 74,132, 51, 75, 134, 53, 82, 77, 135, 83, 138, 57, 260, 98, 139, 85, 146,99, 262, 141, 89, 147, 263, 101, 266, 162, 149, 267, 105, 163, 274, 153,269, 165, 275, 194, 113, 290, 195, 277, 169, 291, 197, 281, 177, 293,322, 201, 323, 297, 209, 325, 386, 305, 329, 387, 225, 389, 337, 393,353, 401, 417, 449 128 7 ≤ K′ < 21 4, 6, 7, 10, 11, 18, 13, 19, 34, 21,35, 25, 37, 66, 67, 41, 69, 130, 49, 73, 131, 133, 81, 258, 137, 259,97, 145, 261, 265, 161, 273, 193, 289, 321, 385 256 2 ≤ K′ < 7 2, 3, 5,9, 17, 33, 65, 129, 257Note: A subchannel number of a selected second-type auxiliary bit isN−X_(j), where j=1, 2, . . . , or J′.

TABLE 7 Correspondence, in the case of N_(max) = 1024, between W_(min)and possible second-type auxiliary bit position numbers ranked indescending order of subchannel numbers N_(max) = 1024 Value rangePossible second-type auxiliary bit subchannel position W_(min) of K′numbers 2 984 ≤ K′ < 1024 512, 768, 896, 960, 992, 1008, 1016, 1020,1022, 1023 4 805 ≤ K′ < 984 256, 384, 448, 480, 496, 504, 508, 510, 511,640, 704, 736, 752, 760, 764, 766, 767, 832, 864, 880, 888, 892, 894,895, 928, 944, 952, 956, 958, 959, 976, 984, 988, 990, 991, 1000, 1004,1006, 1007, 1012, 1014, 1015, 1018, 1019, 1021 8 531 ≤ K′ < 805 128,192, 224, 240, 248, 252, 254, 255, 320, 352, 368, 376, 380, 382, 383,416, 432, 440, 444, 446, 447, 464, 472, 476, 478, 479, 488, 492, 494,495, 500, 502, 503, 506, 507, 509, 576, 608, 624, 632, 636, 638, 639,672, 688, 696, 700, 702, 703, 720, 728, 732, 734, 735, 744, 748, 750,751, 756, 758, 759, 762, 763, 765, 800, 816, 824, 828, 830, 831, 848,856, 860, 862, 863, 872, 876, 878, 879, 884, 886, 887, 890, 891, 893,912, 920, 924, 926, 927, 936, 940, 942, 943, 948, 950, 951, 954, 955,957, 968, 972, 974, 975, 980, 982, 983, 986, 987, 989, 996, 998, 999,1002, 1003, 1005, 1010, 1011, 1013, 1017 16 287 ≤ K′ < 531 64, 96, 112,120, 124, 126, 127, 160, 176, 184, 188, 190, 191, 208, 216, 220, 222,223, 232, 236, 238, 239, 244, 246, 247, 250, 251, 253, 288, 304, 312,316, 318, 319, 336, 344, 348, 350, 351, 360, 364, 366, 367, 372, 374,375, 378, 379, 381, 400, 408, 412, 414, 415, 424, 428, 430, 431, 436,438, 439, 442, 443, 445, 456, 460, 462, 463, 468, 470, 471, 474, 475,477, 484, 486, 487, 490, 491, 493, 498, 499, 501, 505, 544, 560, 568,572, 574, 575, 592, 600, 604, 606, 607, 616, 620, 622, 623, 628, 630,631, 634, 635, 637, 656, 664, 668, 670, 671, 680, 684, 686, 687, 692,694, 695, 698, 699, 701, 712, 716, 718, 719, 724, 726, 727, 730, 731,733, 740, 742, 743, 746, 747, 749, 754, 755, 757, 761, 784, 792, 796,798, 799, 808, 812, 814, 815, 820, 822, 823, 826, 827, 829, 840, 844,846, 847, 852, 854, 855, 858, 859, 861, 868, 870, 871, 874, 875, 877,882, 883, 885, 889, 904, 908, 910, 911, 916, 918, 919, 922, 923, 925,932, 934, 935, 938, 939, 941, 946, 947, 949, 953, 964, 966, 967, 970,971, 973, 978, 979, 981, 985, 994, 995, 997, 1001, 1009 32 134 ≤ K′ <287 32, 48, 56, 60, 62, 63, 80, 88, 92, 94, 95, 104, 108, 110, 111, 116,118, 119, 122, 123, 125, 144, 152, 156, 158, 159, 168, 172, 174, 175,180, 182, 183, 186, 187, 189, 200, 204, 206, 207, 212, 214, 215, 218,219, 221, 228, 230, 231, 234, 235, 237, 242, 243, 245, 249, 272, 280,284, 286, 287, 296, 300, 302, 303, 308, 310, 311, 314, 315, 317, 328,332, 334, 335, 340, 342, 343, 346, 347, 349, 356, 358, 359, 362, 363,365, 370, 371, 373, 377, 392, 396, 398, 399, 404, 406, 407, 410, 411,413, 420, 422, 423, 426, 427, 429, 434, 435, 437, 441, 452, 454, 455,458, 459, 461, 466, 467, 469, 473, 482, 483, 485, 489, 497, 528, 536,540, 542, 543, 552, 556, 558, 559, 564, 566, 567, 570, 571, 573, 584,588, 590, 591, 596, 598, 599, 602, 603, 605, 612, 614, 615, 618, 619,621, 626, 627, 629, 633, 648, 652, 654, 655, 660, 662, 663, 666, 667,669, 676, 678, 679, 682, 683, 685, 690, 691, 693, 697, 708, 710, 711,714, 715, 717, 722, 723, 725, 729, 738, 739, 741, 745, 753, 776, 780,782, 783, 788, 790, 791, 794, 795, 797, 804, 806, 807, 810, 811, 813,818, 819, 821, 825, 836, 838, 839, 842, 843, 845, 850, 851, 853, 857,866, 867, 869, 873, 881, 900, 902, 903, 906, 907, 909, 914, 915, 917,921, 930, 931, 933, 937, 945, 962, 963, 965, 969, 977, 993 64 56 ≤ K′ <134 16, 24, 28, 30, 31, 40, 44, 46, 47, 52, 54, 55, 58, 59, 61, 72, 76,78, 79, 84, 86, 87, 90, 91, 93, 100, 102, 103, 106, 107, 109, 114, 115,117, 121, 136, 140, 142, 143, 148, 150, 151, 154, 155, 157, 164, 166,167, 170, 171, 173, 178, 179, 181, 185, 196, 198, 199, 202, 203, 205,210, 211, 213, 217, 226, 227, 229, 233, 241, 264, 268, 270, 271, 276,278, 279, 282, 283, 285, 292, 294, 295, 298, 299, 301, 306, 307, 309,313, 324, 326, 327, 330, 331, 333, 338, 339, 341, 345, 354, 355, 357,361, 369, 388, 390, 391, 394, 395, 397, 402, 403, 405, 409, 418, 419,421, 425, 433, 450, 451, 453, 457, 465, 481, 520, 524, 526, 527, 532,534, 535, 538, 539, 541, 548, 550, 551, 554, 555, 557, 562, 563, 565,569, 580, 582, 583, 586, 587, 589, 594, 595, 597, 601, 610, 611, 613,617, 625, 644, 646, 647, 650, 651, 653, 658, 659, 661, 665, 674, 675,677, 681, 689, 706, 707, 709, 713, 721, 737, 772, 774, 775, 778, 779,781, 786, 787, 789, 793, 802, 803, 805, 809, 817, 834, 835, 837, 841,849, 865, 898, 899, 901, 905, 913, 929, 961 128 21 ≤ K′ < 56 8, 12, 14,15, 20, 22, 23, 26, 27, 29, 36, 38, 39, 42, 43, 45, 50, 51, 53, 57, 68,70, 71, 74, 75, 77, 82, 83, 85, 89, 98, 99, 101, 105, 113, 132, 134,135, 138, 139, 141, 146, 147, 149, 153, 162, 163, 165, 169, 177, 194,195, 197, 201, 209, 225, 260, 262, 263, 266, 267, 269, 274, 275, 277,281, 290, 291, 293, 297, 305, 322, 323, 325, 329, 337, 353, 386, 387,389, 393, 401, 417, 449, 516, 518, 519, 522, 523, 525, 530, 531, 533,537, 546, 547, 549, 553, 561, 578, 579, 581, 585, 593, 609, 642, 643,645, 649, 657, 673, 705, 770, 771, 773, 777, 785, 801, 833, 897 256 7 ≤K′ < 21 4, 6, 7, 10, 11, 13, 18, 19, 21, 25, 34, 35, 37, 41, 49, 66, 67,69, 73, 81, 97, 130, 131, 133, 137, 145, 161, 193, 258, 259, 261, 265,273, 289, 321, 385, 514, 515, 517, 521, 529, 545, 577, 641, 769 512 2 ≤K′ < 7 2, 3, 5, 9, 17, 33, 65, 129, 257, 513Note: A subchannel number of a selected second-type auxiliary bit isN−X_(j), where j=1, 2, . . . , or J′.

TABLE 8 Correspondence, in the case of N_(max) = 1024, between W_(min)and possible second-type auxiliary bit position numbers ranked indescending order of reliability N_(max) = 1024 Value range Possiblesecond-type auxiliary bit subchannel position W_(min) of K′ numbers 2984 ≤ K′ < 1024 512, 768, 896, 960, 992, 1008, 1016, 1020, 1022, 1023 4805 ≤ K′ < 984 256, 384, 448, 640, 480, 704, 496, 504, 736, 832, 508,752, 510, 511, 864, 760, 764, 880, 928, 766, 888, 767, 944, 892, 894,952, 976, 895, 956, 984, 958, 959, 988, 1000, 990, 1004, 991, 1006,1012, 1007, 1014, 1015, 1018, 1019, 1021 8 531 ≤ K′ < 805 128, 192, 224,320, 240, 352, 248, 576, 252, 368, 416, 254, 376, 255, 608, 432, 380,624, 382, 440, 672, 464, 383, 632, 444, 688, 472, 636, 446, 447, 800,638, 476, 696, 488, 720, 639, 478, 700, 816, 492, 479, 728, 702, 494,824, 500, 703, 732, 495, 848, 744, 502, 828, 734, 503, 856, 748, 830,735, 506, 912, 831, 750, 507, 860, 756, 872, 751, 509, 862, 920, 758,876, 863, 759, 924, 762, 878, 936, 884, 763, 926, 879, 940, 886, 927,765, 968, 887, 942, 890, 948, 943, 972, 891, 950, 974, 893, 951, 980,954, 975, 982, 955, 996, 983, 957, 986, 998, 987, 999, 1002, 989, 1003,1010, 1005, 1011, 1013, 1017 16 287 ≤ K′ < 531 64, 96, 112, 160, 120,176, 124, 288, 126, 184, 208, 127, 188, 304, 216, 190, 312, 191, 544,220, 336, 232, 316, 222, 560, 344, 236, 318, 223, 400, 319, 238, 348,568, 244, 360, 239, 592, 350, 408, 246, 572, 364, 351, 247, 600, 574,412, 250, 366, 424, 372, 656, 575, 251, 604, 414, 367, 616, 428, 374,415, 253, 606, 664, 456, 375, 620, 430, 607, 378, 436, 668, 431, 784,622, 460, 379, 680, 628, 438, 670, 623, 462, 381, 439, 792, 684, 630,468, 671, 442, 463, 712, 631, 686, 470, 443, 796, 634, 692, 808, 484,687, 471, 716, 635, 445, 798, 474, 694, 486, 812, 799, 718, 637, 475,695, 724, 487, 698, 840, 814, 719, 490, 477, 820, 726, 699, 815, 491,844, 740, 822, 727, 498, 701, 730, 493, 846, 904, 823, 742, 499, 852,826, 731, 847, 743, 501, 908, 854, 827, 746, 733, 868, 855, 747, 910,829, 505, 858, 916, 754, 870, 911, 749, 859, 755, 918, 871, 874, 861,932, 919, 757, 922, 875, 934, 882, 923, 761, 877, 935, 964, 883, 938,925, 966, 939, 885, 946, 967, 941, 970, 889, 947, 971, 949, 978, 973,979, 953, 994, 981, 995, 985, 997, 1001, 1009 32 134 ≤ K′ < 287 32, 48,56, 80, 60, 88, 62, 144, 63, 92, 104, 94, 152, 108, 95, 156, 272, 110,168, 116, 158, 111, 280, 172, 118, 159, 200, 119, 174, 284, 122, 180,296, 175, 528, 204, 123, 286, 182, 300, 287, 206, 125, 183, 536, 212,186, 328, 302, 207, 308, 214, 187, 540, 303, 332, 552, 228, 310, 215,189, 542, 218, 334, 392, 311, 230, 556, 340, 543, 314, 219, 335, 231,584, 558, 396, 342, 315, 234, 221, 564, 356, 559, 343, 235, 588, 398,317, 346, 566, 404, 242, 358, 399, 237, 590, 347, 648, 567, 243, 596,406, 359, 570, 591, 362, 349, 420, 407, 245, 652, 598, 571, 410, 363,612, 422, 599, 370, 654, 573, 411, 249, 602, 365, 660, 423, 776, 614,452, 371, 655, 426, 603, 413, 662, 615, 454, 427, 373, 780, 618, 605,676, 663, 434, 455, 666, 619, 429, 782, 458, 377, 678, 435, 788, 626,667, 783, 621, 459, 679, 708, 627, 437, 790, 682, 466, 669, 461, 804,791, 710, 683, 629, 467, 441, 794, 690, 806, 711, 482, 685, 469, 795,714, 633, 691, 807, 483, 836, 810, 715, 797, 473, 693, 722, 485, 838,811, 717, 818, 723, 697, 839, 813, 489, 842, 900, 819, 738, 725, 843,739, 902, 821, 497, 850, 729, 845, 903, 741, 851, 906, 825, 866, 907,853, 745, 914, 867, 909, 857, 915, 753, 869, 930, 917, 873, 931, 921,933, 962, 881, 963, 937, 965, 945, 969, 977, 993 64 56 ≤ K′ < 134 16,24, 28, 40, 30, 44, 31, 72, 46, 52, 47, 76, 54, 78, 136, 55, 84, 58, 79,140, 86, 59, 100, 87, 142, 61, 90, 148, 264, 102, 143, 91, 150, 103,268, 106, 93, 164, 151, 154, 107, 270, 166, 276, 114, 155, 271, 109,167, 520, 196, 115, 278, 170, 157, 292, 279, 198, 171, 117, 524, 282,178, 294, 199, 173, 526, 283, 202, 121, 179, 532, 295, 324, 527, 298,203, 285, 181, 534, 210, 326, 299, 205, 548, 535, 306, 211, 185, 327,538, 301, 330, 550, 388, 307, 226, 213, 539, 331, 551, 227, 580, 390,309, 554, 338, 541, 217, 333, 391, 229, 582, 555, 339, 394, 313, 562,583, 354, 557, 395, 341, 233, 586, 644, 563, 402, 355, 587, 397, 345,646, 565, 403, 241, 594, 357, 589, 647, 418, 595, 405, 650, 569, 361,419, 772, 610, 651, 597, 409, 658, 611, 421, 774, 450, 369, 653, 601,659, 775, 613, 451, 425, 778, 674, 661, 453, 779, 617, 675, 433, 786,665, 781, 457, 677, 787, 706, 625, 802, 707, 789, 681, 465, 803, 709,793, 689, 805, 481, 834, 713, 835, 809, 721, 837, 898, 817, 841, 899,737, 901, 849, 905, 865, 913, 929, 961 128 21 ≤ K′ < 56 8, 12, 14, 20,15, 22, 36, 23, 26, 38, 27, 39, 68, 42, 29, 70, 43, 50, 71, 45, 74, 132,51, 75, 134, 53, 82, 77, 135, 83, 138, 57, 260, 98, 139, 85, 146, 99,262, 141, 89, 147, 263, 101, 266, 162, 149, 267, 105, 163, 516, 274,153, 269, 165, 518, 275, 194, 113, 519, 290, 195, 277, 169, 522, 291,197, 523, 281, 177, 530, 293, 322, 525, 201, 531, 323, 297, 546, 533,209, 325, 547, 386, 305, 537, 329, 549, 387, 225, 578, 579, 389, 553,337, 581, 393, 642, 561, 353, 585, 643, 401, 645, 593, 417, 770, 649,771, 609, 657, 773, 449, 777, 673, 785, 705, 801, 833, 897 256 7 ≤ K′ <21 4, 6, 7, 10, 11, 18, 13, 19, 34, 21, 35, 25, 37, 66, 67, 41, 69, 130,49, 73, 131, 133, 81, 258, 137, 259, 97, 145, 261, 265, 161, 514, 515,273, 517, 193, 289, 521, 529, 321, 545, 385, 577, 641, 769 512 2 ≤ K′ <7 2, 3, 5, 9, 17, 33, 65, 129, 257, 513Note: A subchannel number of a selected second-type auxiliary bit isN−X_(j), where j=1, 2, . . . , or J′.

TABLE 9 Correspondence, in the case of N_(max) = 512, between an indexand possible second-type auxiliary bit position numbers ranked indescending order of subchannel numbers N_(max) = 512 Index Value rangePossible second-type auxiliary bit subchannel position number of K′numbers 1 487 ≤ K′ < 512 256, 384, 448, 480, 496, 504, 508, 510, 511 2387 ≤ K′ < 487 128, 192, 224, 240, 248, 252, 254, 255, 320, 352, 368,376, 380, 382, 383, 416, 432, 440, 444, 446, 447, 464, 472, 476, 478,479, 488, 492, 494, 495, 500, 502, 503, 506, 507, 509 3 243 ≤ K′ < 38764, 96, 112, 120, 124, 126, 127, 160, 176, 184, 188, 190, 191, 208, 216,220, 222, 223, 232, 236, 238, 239, 244, 246, 247, 250, 251, 253, 288,304, 312, 316, 318, 319, 336, 344, 348, 350, 351, 360, 364, 366, 367,372, 374, 375, 378, 379, 381, 400, 408, 412, 414, 415, 424, 428, 430,431, 436, 438, 439, 442, 443, 445, 456, 460, 462, 463, 468, 470, 471,474, 475, 477, 484, 486, 487, 490, 491, 493, 498, 499, 501, 505 4 125 ≤K′ < 243 32, 48, 56, 60, 62, 63, 80, 88, 92, 94, 95, 104, 108, 110, 111,116, 118, 119, 122, 123, 125, 144, 152, 156, 158, 159, 168, 172, 174,175, 180, 182, 183, 186, 187, 189, 200, 204, 206, 207, 212, 214, 215,218, 219, 221, 228, 230, 231, 234, 235, 237, 242, 243, 245, 249, 272,280, 284, 286, 287, 296, 300, 302, 303, 308, 310, 311, 314, 315, 317,328, 332, 334, 335, 340, 342, 343, 346, 347, 349, 356, 358, 359, 362,363, 365, 370, 371, 373, 377, 392, 396, 398, 399, 404, 406, 407, 410,411, 413, 420, 422, 423, 426, 427, 429, 434, 435, 437, 441, 452, 454,455, 458, 459, 461, 466, 467, 469, 473, 482, 483, 485, 489, 497 5 55 ≤K′ < 125 16, 24, 28, 30, 31, 40, 44, 46, 47, 52, 54, 55, 58, 59, 61, 72,76, 78, 79, 84, 86, 87, 90, 91, 93, 100, 102, 103, 106, 107, 109, 114,115, 117, 121, 136, 140, 142, 143, 148, 150, 151, 154, 155, 157, 164,166, 167, 170, 171, 173, 178, 179, 181, 185, 196, 198, 199, 202, 203,205, 210, 211, 213, 217, 226, 227, 229, 233, 241, 264, 268, 270, 271,276, 278, 279, 282, 283, 285, 292, 294, 295, 298, 299, 301, 306, 307,309, 313, 324, 326, 327, 330, 331, 333, 338, 339, 341, 345, 354, 355,357, 361, 369, 388, 390, 391, 394, 395, 397, 402, 403, 405, 409, 418,419, 421, 425, 433, 450, 451, 453, 457, 465, 481 6 21 ≤ K′ < 55 8, 12,14, 15, 20, 22, 23, 26, 27, 29, 36, 38, 39, 42, 43, 45, 50, 51, 53, 57,68, 70, 71, 74, 75, 77, 82, 83, 85, 89, 98, 99, 101, 105, 113, 132, 134,135, 138, 139, 141, 146, 147, 149, 153, 162, 163, 165, 169, 177, 194,195, 197, 201, 209, 225, 260, 262, 263, 266, 267, 269, 274, 275, 277,281, 290, 291, 293, 297, 305, 322, 323, 325, 329, 337, 353, 386, 387,389, 393, 401, 417, 449 7 7 ≤ K′ < 21 4, 6, 7, 10, 11, 13, 18, 19, 21,25, 34, 35, 37, 41, 49, 66, 67, 69, 73, 81, 97, 130, 131, 133, 137, 145,161, 193, 258, 259, 261, 265, 273, 289, 321, 385 8 2 ≤ K′ < 7 2, 3, 5,9, 17, 33, 65, 129, 257Note: A subchannel number of a selected second-type auxiliary bit isN−X_(j), where j=1, 2, . . . , or J′.

TABLE 10 Correspondence, in the case of N_(max) = 512, between an indexand possible second-type auxiliary bit position numbers ranked indescending order of reliability N_(max) = 512 Index Value range Possiblesecond-type auxiliary bit subchannel position number of K′ numbers 1 487≤ K′ < 512 256, 384, 448, 480, 496, 504, 508, 510, 511 2 387 ≤ K′ < 487128, 192, 224, 320, 240, 352, 248, 252, 368, 416, 254, 376, 255, 432,380, 382, 440, 464, 383, 444, 472, 446, 447, 476, 488, 478, 492, 479,494, 500, 495, 502, 503, 506, 507, 509 3 243 ≤ K′ < 387 64, 96, 112,160, 120, 176, 124, 288, 126, 184, 208, 127, 188, 304, 216, 190, 312,191, 220, 336, 232, 316, 222, 344, 236, 318, 223, 400, 319, 238, 348,244, 360, 239, 350, 408, 246, 364, 351, 247, 412, 250, 366, 424, 372,251, 414, 367, 428, 374, 415, 253, 456, 375, 430, 378, 436, 431, 460,379, 438, 462, 381, 439, 468, 442, 463, 470, 443, 484, 471, 445, 474,486, 475, 487, 490, 477, 491, 498, 493, 499, 501, 505 4 125 ≤ K′ < 24332, 48, 56, 80, 60, 88, 62, 144, 63, 92, 104, 94, 152, 108, 95, 156,272, 110, 168, 116, 158, 111, 280, 172, 118, 159, 200, 119, 174, 284,122, 180, 296, 175, 204, 123, 286, 182, 300, 287, 206, 125, 183, 212,186, 328, 302, 207, 308, 214, 187, 303, 332, 228, 310, 215, 189, 218,334, 392, 311, 230, 340, 314, 219, 335, 231, 396, 342, 315, 234, 221,356, 343, 235, 398, 317, 346, 404, 242, 358, 399, 237, 347, 243, 406,359, 362, 349, 420, 407, 245, 410, 363, 422, 370, 411, 249, 365, 423,452, 371, 426, 413, 454, 427, 373, 434, 455, 429, 458, 377, 435, 459,437, 466, 461, 467, 441, 482, 469, 483, 473, 485, 489, 497 5 55 ≤ K′ <125 16, 24, 28, 40, 30, 44, 31, 72, 46, 52, 47, 76, 54, 78, 136, 55, 84,58, 79, 140, 86, 59, 100, 87, 142, 61, 90, 148, 264, 102, 143, 91, 150,103, 268, 106, 93, 164, 151, 154, 107, 270, 166, 276, 114, 155, 271,109, 167, 196, 115, 278, 170, 157, 292, 279, 198, 171, 117, 282, 178,294, 199, 173, 283, 202, 121, 179, 295, 324, 298, 203, 285, 181, 210,326, 299, 205, 306, 211, 185, 327, 301, 330, 388, 307, 226, 213, 331,227, 390, 309, 338, 217, 333, 391, 229, 339, 394, 313, 354, 395, 341,233, 402, 355, 397, 345, 403, 241, 357, 418, 405, 361, 419, 409, 421,450, 369, 451, 425, 453, 433, 457, 465, 481 6 21 ≤ K′ < 55 8, 12, 14,20, 15, 22, 36, 23, 26, 38, 27, 39, 68, 42, 29, 70, 43, 50, 71, 45, 74,132, 51, 75, 134, 53, 82, 77, 135, 83, 138, 57, 260, 98, 139, 85, 146,99, 262, 141, 89, 147, 263, 101, 266, 162, 149, 267, 105, 163, 274, 153,269, 165, 275, 194, 113, 290, 195, 277, 169, 291, 197, 281, 177, 293,322, 201, 323, 297, 209, 325, 386, 305, 329, 387, 225, 389, 337, 393,353, 401, 417, 449 7 7 ≤ K′ < 21 4, 6, 7, 10, 11, 18, 13, 19, 34, 21,35, 25, 37, 66, 67, 41, 69, 130, 49, 73, 131, 133, 81, 258, 137, 259,97, 145, 261, 265, 161, 273, 193, 289, 321, 385 8 2 ≤ K′ < 7 2, 3, 5, 9,17, 33, 65, 129, 257Note: A subchannel number of a selected second-type auxiliary bit isN−X_(j), where j=1, 2, . . . , or J′.

TABLE 11 Correspondence, in the case of N_(max) = 1024, between an indexand possible second-type auxiliary bit position numbers ranked indescending order of subchannel numbers N_(max) = 1024 Index Value rangePossible second-type auxiliary bit subchannel position number of K′numbers 1 984 ≤ K′ < 1024 512, 768, 896, 960, 992, 1008, 1016, 1020,1022, 1023 2 805 ≤ K′ < 984 256, 384, 448, 480, 496, 504, 508, 510, 511,640, 704, 736, 752, 760, 764, 766, 767, 832, 864, 880, 888, 892, 894,895, 928, 944, 952, 956, 958, 959, 976, 984, 988, 990, 991, 1000, 1004,1006, 1007, 1012, 1014, 1015, 1018, 1019, 1021 3 531 ≤ K′ < 805 128,192, 224, 240, 248, 252, 254, 255, 320, 352, 368, 376, 380, 382, 383,416, 432, 440, 444, 446, 447, 464, 472, 476, 478, 479, 488, 492, 494,495, 500, 502, 503, 506, 507, 509, 576, 608, 624, 632, 636, 638, 639,672, 688, 696, 700, 702, 703, 720, 728, 732, 734, 735, 744, 748, 750,751, 756, 758, 759, 762, 763, 765, 800, 816, 824, 828, 830, 831, 848,856, 860, 862, 863, 872, 876, 878, 879, 884, 886, 887, 890, 891, 893,912, 920, 924, 926, 927, 936, 940, 942, 943, 948, 950, 951, 954, 955,957, 968, 972, 974, 975, 980, 982, 983, 986, 987, 989, 996, 998, 999,1002, 1003, 1005, 1010, 1011, 1013, 1017 4 287 ≤ K′ < 531 64, 96, 112,120, 124, 126, 127, 160, 176, 184, 188, 190, 191, 208, 216, 220, 222,223, 232, 236, 238, 239, 244, 246, 247, 250, 251, 253, 288, 304, 312,316, 318, 319, 336, 344, 348, 350, 351, 360, 364, 366, 367, 372, 374,375, 378, 379, 381, 400, 408, 412, 414, 415, 424, 428, 430, 431, 436,438, 439, 442, 443, 445, 456, 460, 462, 463, 468, 470, 471, 474, 475,477, 484, 486, 487, 490, 491, 493, 498, 499, 501, 505, 544, 560, 568,572, 574, 575, 592, 600, 604, 606, 607, 616, 620, 622, 623, 628, 630,631, 634, 635, 637, 656, 664, 668, 670, 671, 680, 684, 686, 687, 692,694, 695, 698, 699, 701, 712, 716, 718, 719, 724, 726, 727, 730, 731,733, 740, 742, 743, 746, 747, 749, 754, 755, 757, 761, 784, 792, 796,798, 799, 808, 812, 814, 815, 820, 822, 823, 826, 827, 829, 840, 844,846, 847, 852, 854, 855, 858, 859, 861, 868, 870, 871, 874, 875, 877,882, 883, 885, 889, 904, 908, 910, 911, 916, 918, 919, 922, 923, 925,932, 934, 935, 938, 939, 941, 946, 947, 949, 953, 964, 966, 967, 970,971, 973, 978, 979, 981, 985, 994, 995, 997, 1001, 1009 5 134 ≤ K′ < 28732, 48, 56, 60, 62, 63, 80, 88, 92, 94, 95, 104, 108, 110, 111, 116,118, 119, 122, 123, 125, 144, 152, 156, 158, 159, 168, 172, 174, 175,180, 182, 183, 186, 187, 189, 200, 204, 206, 207, 212, 214, 215, 218,219, 221, 228, 230, 231, 234, 235, 237, 242, 243, 245, 249, 272, 280,284, 286, 287, 296, 300, 302, 303, 308, 310, 311, 314, 315, 317, 328,332, 334, 335, 340, 342, 343, 346, 347, 349, 356, 358, 359, 362, 363,365, 370, 371, 373, 377, 392, 396, 398, 399, 404, 406, 407, 410, 411,413, 420, 422, 423, 426, 427, 429, 434, 435, 437, 441, 452, 454, 455,458, 459, 461, 466, 467, 469, 473, 482, 483, 485, 489, 497, 528, 536,540, 542, 543, 552, 556, 558, 559, 564, 566, 567, 570, 571, 573, 584,588, 590, 591, 596, 598, 599, 602, 603, 605, 612, 614, 615, 618, 619,621, 626, 627, 629, 633, 648, 652, 654, 655, 660, 662, 663, 666, 667,669, 676, 678, 679, 682, 683, 685, 690, 691, 693, 697, 708, 710, 711,714, 715, 717, 722, 723, 725, 729, 738, 739, 741, 745, 753, 776, 780,782, 783, 788, 790, 791, 794, 795, 797, 804, 806, 807, 810, 811, 813,818, 819, 821, 825, 836, 838, 839, 842, 843, 845, 850, 851, 853, 857,866, 867, 869, 873, 881, 900, 902, 903, 906, 907, 909, 914, 915, 917,921, 930, 931, 933, 937, 945, 962, 963, 965, 969, 977, 993 6 56 ≤ K′ <134 16, 24, 28, 30, 31, 40, 44, 46, 47, 52, 54, 55, 58, 59, 61, 72, 76,78, 79, 84, 86, 87, 90, 91, 93, 100, 102, 103, 106, 107, 109, 114, 115,117, 121, 136, 140, 142, 143, 148, 150, 151, 154, 155, 157, 164, 166,167, 170, 171, 173, 178, 179, 181, 185, 196, 198, 199, 202, 203, 205,210, 211, 213, 217, 226, 227, 229, 233, 241, 264, 268, 270, 271, 276,278, 279, 282, 283, 285, 292, 294, 295, 298, 299, 301, 306, 307, 309,313, 324, 326, 327, 330, 331, 333, 338, 339, 341, 345, 354, 355, 357,361, 369, 388, 390, 391, 394, 395, 397, 402, 403, 405, 409, 418, 419,421, 425, 433, 450, 451, 453, 457, 465, 481, 520, 524, 526, 527, 532,534, 535, 538, 539, 541, 548, 550, 551, 554, 555, 557, 562, 563, 565,569, 580, 582, 583, 586, 587, 589, 594, 595, 597, 601, 610, 611, 613,617, 625, 644, 646, 647, 650, 651, 653, 658, 659, 661, 665, 674, 675,677, 681, 689, 706, 707, 709, 713, 721, 737, 772, 774, 775, 778, 779,781, 786, 787, 789, 793, 802, 803, 805, 809, 817, 834, 835, 837, 841,849, 865, 898, 899, 901, 905, 913, 929, 961 7 21 ≤ K′ < 56 8, 12, 14,15, 20, 22, 23, 26, 27, 29, 36, 38, 39, 42, 43, 45, 50, 51, 53, 57, 68,70, 71, 74, 75, 77, 82, 83, 85, 89, 98, 99, 101, 105, 113, 132, 134,135, 138, 139, 141, 146, 147, 149, 153, 162, 163, 165, 169, 177, 194,195, 197, 201, 209, 225, 260, 262, 263, 266, 267, 269, 274, 275, 277,281, 290, 291, 293, 297, 305, 322, 323, 325, 329, 337, 353, 386, 387,389, 393, 401, 417, 449, 516, 518, 519, 522, 523, 525, 530, 531, 533,537, 546, 547, 549, 553, 561, 578, 579, 581, 585, 593, 609, 642, 643,645, 649, 657, 673, 705, 770, 771, 773, 777, 785, 801, 833, 897 8 7 ≤ K′< 21 4, 6, 7, 10, 11, 13, 18, 19, 21, 25, 34, 35, 37, 41, 49, 66, 67,69, 73, 81, 97, 130, 131, 133, 137, 145, 161, 193, 258, 259, 261, 265,273, 289, 321, 385, 514, 515, 517, 521, 529, 545, 577, 641, 769 9 2 ≤ K′< 7 2, 3, 5, 9, 17, 33, 65, 129, 257, 513Note: A subchannel number of a selected second-type auxiliary bit isN−X_(j), where j=1, 2, . . . , or J′.

TABLE 12 Correspondence, in the case of N_(max) = 1024, between an indexand possible second-type auxiliary bit position numbers ranked indescending order of reliability N_(max) = 1024 Index Value rangePossible second-type auxiliary bit subchannel position number of K′numbers Q_(j) 1 984 ≤ K′ < 1024 512, 768, 896, 960, 992, 1008, 1016,1020, 1022, 1023 2 805 ≤ K′ < 984 256, 384, 448, 640, 480, 704, 496,504, 736, 832, 508, 752, 510, 511, 864, 760, 764, 880, 928, 766, 888,767, 944, 892, 894, 952, 976, 895, 956, 984, 958, 959, 988, 1000, 990,1004, 991, 1006, 1012, 1007, 1014, 1015, 1018, 1019, 1021 3 531 ≤ K′ <805 128, 192, 224, 320, 240, 352, 248, 576, 252, 368, 416, 254, 376,255, 608, 432, 380, 624, 382, 440, 672, 464, 383, 632, 444, 688, 472,636, 446, 447, 800, 638, 476, 696, 488, 720, 639, 478, 700, 816, 492,479, 728, 702, 494, 824, 500, 703, 732, 495, 848, 744, 502, 828, 734,503, 856, 748, 830, 735, 506, 912, 831, 750, 507, 860, 756, 872, 751,509, 862, 920, 758, 876, 863, 759, 924, 762, 878, 936, 884, 763, 926,879, 940, 886, 927, 765, 968, 887, 942, 890, 948, 943, 972, 891, 950,974, 893, 951, 980, 954, 975, 982, 955, 996, 983, 957, 986, 998, 987,999, 1002, 989, 1003, 1010, 1005, 1011, 1013, 1017 4 287 ≤ K′ < 531 64,96, 112, 160, 120, 176, 124, 288, 126, 184, 208, 127, 188, 304, 216,190, 312, 191, 544, 220, 336, 232, 316, 222, 560, 344, 236, 318, 223,400, 319, 238, 348, 568, 244, 360, 239, 592, 350, 408, 246, 572, 364,351, 247, 600, 574, 412, 250, 366, 424, 372, 656, 575, 251, 604, 414,367, 616, 428, 374, 415, 253, 606, 664, 456, 375, 620, 430, 607, 378,436, 668, 431, 784, 622, 460, 379, 680, 628, 438, 670, 623, 462, 381,439, 792, 684, 630, 468, 671, 442, 463, 712, 631, 686, 470, 443, 796,634, 692, 808, 484, 687, 471, 716, 635, 445, 798, 474, 694, 486, 812,799, 718, 637, 475, 695, 724, 487, 698, 840, 814, 719, 490, 477, 820,726, 699, 815, 491, 844, 740, 822, 727, 498, 701, 730, 493, 846, 904,823, 742, 499, 852, 826, 731, 847, 743, 501, 908, 854, 827, 746, 733,868, 855, 747, 910, 829, 505, 858, 916, 754, 870, 911, 749, 859, 755,918, 871, 874, 861, 932, 919, 757, 922, 875, 934, 882, 923, 761, 877,935, 964, 883, 938, 925, 966, 939, 885, 946, 967, 941, 970, 889, 947,971, 949, 978, 973, 979, 953, 994, 981, 995, 985, 997, 1001, 1009 5 134≤ K′ < 287 32, 48, 56, 80, 60, 88, 62, 144, 63, 92, 104, 94, 152, 108,95, 156, 272, 110, 168, 116, 158, 111, 280, 172, 118, 159, 200, 119,174, 284, 122, 180, 296, 175, 528, 204, 123, 286, 182, 300, 287, 206,125, 183, 536, 212, 186, 328, 302, 207, 308, 214, 187, 540, 303, 332,552, 228, 310, 215, 189, 542, 218, 334, 392, 311, 230, 556, 340, 543,314, 219, 335, 231, 584, 558, 396, 342, 315, 234, 221, 564, 356, 559,343, 235, 588, 398, 317, 346, 566, 404, 242, 358, 399, 237, 590, 347,648, 567, 243, 596, 406, 359, 570, 591, 362, 349, 420, 407, 245, 652,598, 571, 410, 363, 612, 422, 599, 370, 654, 573, 411, 249, 602, 365,660, 423, 776, 614, 452, 371, 655, 426, 603, 413, 662, 615, 454, 427,373, 780, 618, 605, 676, 663, 434, 455, 666, 619, 429, 782, 458, 377,678, 435, 788, 626, 667, 783, 621, 459, 679, 708, 627, 437, 790, 682,466, 669, 461, 804, 791, 710, 683, 629, 467, 441, 794, 690, 806, 711,482, 685, 469, 795, 714, 633, 691, 807, 483, 836, 810, 715, 797, 473,693, 722, 485, 838, 811, 717, 818, 723, 697, 839, 813, 489, 842, 900,819, 738, 725, 843, 739, 902, 821, 497, 850, 729, 845, 903, 741, 851,906, 825, 866, 907, 853, 745, 914, 867, 909, 857, 915, 753, 869, 930,917, 873, 931, 921, 933, 962, 881, 963, 937, 965, 945, 969, 977, 993 656 ≤ K′ < 134 16, 24, 28, 40, 30, 44, 31, 72, 46, 52, 47, 76, 54, 78,136, 55, 84, 58, 79, 140, 86, 59, 100, 87, 142, 61, 90, 148, 264, 102,143, 91, 150, 103, 268, 106, 93, 164, 151, 154, 107, 270, 166, 276, 114,155, 271, 109, 167, 520, 196, 115, 278, 170, 157, 292, 279, 198, 171,117, 524, 282, 178, 294, 199, 173, 526, 283, 202, 121, 179, 532, 295,324, 527, 298, 203, 285, 181, 534, 210, 326, 299, 205, 548, 535, 306,211, 185, 327, 538, 301, 330, 550, 388, 307, 226, 213, 539, 331, 551,227, 580, 390, 309, 554, 338, 541, 217, 333, 391, 229, 582, 555, 339,394, 313, 562, 583, 354, 557, 395, 341, 233, 586, 644, 563, 402, 355,587, 397, 345, 646, 565, 403, 241, 594, 357, 589, 647, 418, 595, 405,650, 569, 361, 419, 772, 610, 651, 597, 409, 658, 611, 421, 774, 450,369, 653, 601, 659, 775, 613, 451, 425, 778, 674, 661, 453, 779, 617,675, 433, 786, 665, 781, 457, 677, 787, 706, 625, 802, 707, 789, 681,465, 803, 709, 793, 689, 805, 481, 834, 713, 835, 809, 721, 837, 898,817, 841, 899, 737, 901, 849, 905, 865, 913, 929, 961 7 21 ≤ K′ < 56 8,12, 14, 20, 15, 22, 36, 23, 26, 38, 27, 39, 68, 42, 29, 70, 43, 50, 71,45, 74, 132, 51, 75, 134, 53, 82, 77, 135, 83, 138, 57, 260, 98, 139,85, 146, 99, 262, 141, 89, 147, 263, 101, 266, 162, 149, 267, 105, 163,516, 274, 153, 269, 165, 518, 275, 194, 113, 519, 290, 195, 277, 169,522, 291, 197, 523, 281, 177, 530, 293, 322, 525, 201, 531, 323, 297,546, 533, 209, 325, 547, 386, 305, 537, 329, 549, 387, 225, 578, 579,389, 553, 337, 581, 393, 642, 561, 353, 585, 643, 401, 645, 593, 417,770, 649, 771, 609, 657, 773, 449, 777, 673, 785, 705, 801, 833, 897 8 7≤ K′ < 21 4, 6, 7, 10, 11, 18, 13, 19, 34, 21, 35, 25, 37, 66, 67, 41,69, 130, 49, 73, 131, 133, 81, 258, 137, 259, 97, 145, 261, 265, 161,514, 515, 273, 517, 193, 289, 521, 529, 321, 545, 385, 577, 641, 769 9 2≤ K′ < 7 2, 3, 5, 9, 17, 33, 65, 129, 257, 513Note: A subchannel number of a selected second-type auxiliary bit isN−X_(j), where j=1, 2, . . . , or J′.

What is claimed is:
 1. A method for communicating information in awireless communication network, comprising: obtaining, by acommunication device, K bits of information, wherein K≥1; generating, bythe communication device, a to-be-encoded sequence u₁ ^(N), wherein thesequence u₁ ^(N) comprises N bits, each bit of the sequence u₁ ^(N)corresponds to a subchannel, and each subchannel has a reliability,wherein the K information bits, a quantity J of first-type auxiliarybits, and a quantity J′ of second-type auxiliary bits are placed inK′=K+J+J′ bit positions of the sequence u₁ ^(N) according toreliabilities of the subchannels, wherein N≥K′, and N is an integerpower of 2; encoding, by the communication device, the sequence u₁ ^(N)in an encoding process, to obtain an output sequence; and transmitting,by the communication device, the output sequence.
 2. The methodaccording to claim 1, wherein the first-type auxiliary bits are cyclicredundancy check (CRC) bits.
 3. The method according to claim 1, whereinthe second-type auxiliary bits are parity check bits.
 4. The methodaccording to claim 3, wherein J′=3.
 5. The method according to claim 3,wherein when N=64 and 19≤K′≤38, the J′ parity check bits aresuccessively placed in J′ of the following bit positions of the sequenceu₁ ^(N): {56, 52, 50, 49, 44, 42, 41, 38, 37, 35, 28, 26, 25, 22, 21,19, 14, 13, 11, 7}.
 6. The method according to claim 1, wherein encodingthe sequence u₁ ^(N) in an encoding process, to obtain an outputsequence comprises: encoding the sequence u₁ ^(N) in a polar codingprocess x₁ ^(N)=u₁ ^(N)G_(N), to obtain an encoded sequence x₁ ^(N),wherein G_(N) is a polar code generator matrix of N rows×N columns; andrate matching the encoded sequence x₁ ^(N), to obtain a rate-matchedencoded sequence, wherein the rate-matched encoded sequence comprises Mbits, M≤N, and wherein the rate-matched encoded sequence is output asthe output sequence.
 7. The method according to claim 6, wherein ratematching the encoded sequence x₁ ^(N) comprises: when N>M, selecting N−Mbits in the encoded sequence x₁ ^(N) as punctured bits; and removing thepunctured bits from the encoded sequence x₁ ^(N); wherein the puncturedbits are selected according to reliabilities of the subchannelscorresponding to the bit positions of the encoded sequence x₁ ^(N), andwherein the information bits, the first-type auxiliary bits, and thesecond-type auxiliary bits are not selected as the punctured bits. 8.The method according to claim 7, wherein each row of the polar generatormatrix G_(N) has a row weight, and W_(min) is a minimum row weight ofrows in the polar generator matrix G_(N) that correspond to the Kinformation bits, J first-type auxiliary bits, and J′ second-typeauxiliary bits in the sequence u₁ ^(N), K′=K+J+J′, wherein the K′ bitsin the sequence u₁ ^(N) correspond to K′ subchannels, and eachsubchannel has a subchannel number, and wherein the J′ bit positions forplacing the J′ second-type auxiliary bits are selected among the K′ bitpositions, in descending order of subchannel numbers, from bit positionscorresponding to rows in the polar generator matrix G_(N) having theminimum row weight W_(min).
 9. The method according to claim 7, whereinW_(min) is a minimum row weight of rows in the polar generator matrixG_(N) that correspond to the K information bits, J first-type auxiliarybits, and J′ second-type auxiliary bits in the sequence u₁ ^(N),K′=K+J+J′, wherein the K′ bits in the sequence u₁ ^(N) correspond to K′subchannels, and each subchannel has a reliability, and wherein the J′bit positions for placing the J′ second-type auxiliary bits are selectedamong the K′ bit positions, in descending order of reliability, from bitpositions corresponding to rows in the polar generator matrix G_(N)having the minimum row weight W_(min).
 10. An apparatus, comprising aprocessor and a communication interface; wherein the processor isconfigured to: obtain K bits of information, wherein K≥1; generate ato-be-encoded sequence u₁ ^(N), wherein the sequence u₁ ^(N) comprises Nbits, and N is an integer power of 2; and encode the sequence u₁ ^(N) inan encoding process, to obtain an output sequence; wherein thecommunication interface is configured to: output the output sequence;wherein each bit of the sequence u₁ ^(N) corresponds to a subchannel,and each subchannel has a reliability; wherein the K information bits, aquantity J of first-type auxiliary bits, and a quantity J′ ofsecond-type auxiliary bits are placed in K′=K+J+J′ bit positions of thesequence u₁ ^(N) according to reliabilities of the subchannels, whereinN≥K′.
 11. The apparatus according to claim 10, wherein the first-typeauxiliary bits are cyclic redundancy check (CRC) bits.
 12. The apparatusaccording to claim 10, wherein the second-type auxiliary bits are paritycheck bits.
 13. The apparatus according to claim 12, wherein J′=3. 14.The apparatus according to claim 12, wherein when N=64 and 19≤K′≤38, theJ′ parity check bits are successively placed in J′ of the following bitpositions of the sequence u₁ ^(N): {56, 52, 50, 49, 44, 42, 41, 38, 37,35, 28, 26, 25, 22, 21, 19, 14, 13, 11, 7}.
 15. The apparatus accordingto claim 10, wherein in encoding the sequence u₁ ^(N), the processor isconfigured to: encode the sequence u₁ ^(N) in a polar coding process x₁^(N)=u₁ ^(N)G_(N), to obtain an encoded sequence x₁ ^(N), wherein G_(N)is a polar code generator matrix of N rows×N columns; and rate match theencoded sequence x₁ ^(N), to obtain a rate-matched encoded sequence;wherein the rate-matched encoded sequence comprises M bits, M≤N, andwherein the rate-matched encoded sequence is output as the outputsequence.
 16. The apparatus according to claim 15, wherein in ratematching the encoded sequence x₁ ^(N), the processor is configured to:when N>M, select N−M bits in the encoded sequence x₁ ^(N) as puncturedbits; and remove the punctured bits from the encoded sequence x₁ ^(N),wherein the punctured bits are selected according to reliabilities ofthe subchannels corresponding to the bit positions of the encodedsequence x₁ ^(N), and wherein the information bits, the first-typeauxiliary bits, and the second-type auxiliary bits are not selected asthe punctured bits.
 17. The apparatus according to claim 16, whereineach row of the polar generator matrix G_(N) has a row weight, andW_(min) is a minimum row weight of rows in the polar generator matrixG_(N) that correspond to the K information bits, J first-type auxiliarybits, and J′ second-type auxiliary bits in the sequence u₁ ^(N),K′=K+J+J′, wherein the K′ bits in the sequence u₁ ^(N) correspond to K′subchannels, and each subchannel has a subchannel number, wherein the J′bit positions for placing the J′ second-type auxiliary bits are selectedamong the K′ bit positions, in descending order of subchannel numbers,from bit positions corresponding to rows in the polar generator matrixG_(N) having the minimum row weight W_(min).
 18. The apparatus accordingto claim 16, wherein W_(min) is a minimum row weight of rows in thepolar generator matrix G_(N) that correspond to the K information bits,J first-type auxiliary bits, and J′ second-type auxiliary bits in thesequence u₁ ^(N), K′=K+J+J′, wherein the K′ bits in the sequence u₁ ^(N)correspond to K′ subchannels, and each subchannel has a reliability,wherein the J′ bit positions for placing the J′ second-type auxiliarybits are selected among the K′ bit positions, in descending order ofreliability, from bit positions corresponding to rows in the polargenerator matrix G_(N) having the minimum row weight W_(min).
 19. Anon-transitory storage medium storing computer-executable instructionswhich, when executed by a processor of a communication device, cause thecommunication device to: obtain K bits of information, wherein K≥1;generate a to-be-encoded sequence u₁ ^(N), wherein N is a length of thesequence, and N is an integer power of 2; encode the sequence u₁ ^(N) inan encoding process, to obtain an output sequence; and transmit theoutput sequence; wherein the sequence u₁ ^(N) comprises N bits, each bitof the sequence u₁ ^(N) corresponds to a subchannel, and each subchannelhas a reliability, wherein the K information bits, a quantity J offirst-type auxiliary bits, and a quantity J′ of second-type auxiliarybits are placed in K′=K+J+J′ bit positions of the sequence u₁ ^(N)according to reliabilities of the subchannels, wherein N≥K′.
 20. Thenon-transitory storage medium according to claim 19, wherein thesecond-type auxiliary bits are parity check bits.
 21. The non-transitorystorage medium according to claim 20, wherein J′=3.
 22. Thenon-transitory storage medium according to claim 20, wherein when N=64and 19≤K′≤38, the J′ parity check bits are successively placed in J′ ofthe following bit positions of the sequence u₁ ^(N): {56, 52, 50, 49,44, 42, 41, 38, 37, 35, 28, 26, 25, 22, 21, 19, 14, 13, 11, 7}.